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Inflation forecasting and the crisis: assessingthe impact on the performance of different

forecasting models and methods

Christian Buelens*

Abstract: This paper analyses how the accuracy of euro area inflation forecasting models has

been affected by the financial and economic crisis. Its first objective is to compare the

precision of three representative groups of inflation forecasting models (rules of thumb and

benchmark models; autoregressive moving average models; autoregressive distributed lag

models) under a direct and an indirect approach, respectively. Under the former, theforecasting models contain headline inflation as their dependent variable; under the latter,

individual forecasts are generated in a first step for each of the main HICP components, and

subsequently aggregated to obtain an indirect forecast of headline inflation. The second

objective is to study how the absolute and relative forecasting performances of the models and

approaches have been impacted by the economic and financial crisis.

The paper finds that direct forecasting models selected on the basis of a penalty function

generally dominate simple rules of thumb and econometric benchmark models. The analysis

furthermore suggests that when an appropriate specification for the component-specific

models is found, indirect forecasts outperform the corresponding direct forecasts.

Nonetheless, in line with the findings from earlier studies, there are insufficient elements toassert a systematic superiority of one of the two approaches. Concerning the second objective,

the across-the-board rise in the forecast errors of all models considered, confirms that

inflation forecasting has become substantially more difficult after the onset of the crisis.

However, the deterioration of the different models has been uneven. Relative to simple

econometric models and rules of thumb, the performance of direct autoregressive distributed

lag models and of the indirect approach has improved during the crisis.

Keywords: HICP, inflation, forecasting, aggregation, model selection, model evaluation,

inflation targeting

JEL Codes: C32, C52, C53, E31, E37, E58

* E-mail: [email protected]

A first version of this paper was written when I was working at the Directorate General for Economic and

Financial Affairs of the European Commission. I thank Björn Döhring, Luis Fau, Cecilia Frale, Paul Kutos,

Francesco Montaruli and Alessandra Tucci for comments on an earlier draft of this paper. The opinionsexpressed herein and any errors are my own.



2

1. Introduction

Economic agents base many current decisions inter alia on their expectation of the future

inflation pattern. The views held about future inflation may influence firms' price-settingbehaviour or workers' wage-demands, and thereby impact current purchasing power and

labour costs; through its effect on the real interest rate and on inflation risk premia, the

expected inflation rate furthermore influences savings and investment decisions. Inflation

forecasts and projections are also often at the heart of economic policy decision-making, as is

the case for monetary policy, which in most industrialised economies is mandated to maintain

price stability over the medium term. Decision-makers hence need to have a view on the

likely future path of inflation when taking measures that are necessary to reach their objective.

Yet, while being indispensable to many decision-making agents, forming inflation

expectations is generally both complex and costly: indeed, inflation forecasting requires an

understanding of economic relationships, econometric modelling tools, access to data and

other information.

The first objective of this paper is to assess the forecasting performance of direct and indirect

euro area inflation forecasting models. While direct inflation forecasting models contain

headline inflation as their dependent variable, indirect forecasts are obtained by aggregating

component-specific forecasts, weighted by their share in the Harmonised Index of Consumer

Prices (HICP).1

The models considered in the paper are taken from three different model

groups (rules of thumb and benchmark models; autoregressive moving average models;

autoregressive distributed lag models), which vary in terms of selection procedure and

information included. As such, they are simple but representative illustrations of the more

sophisticated models used by forecasters in practice.

The first group of models comprises "low-cost" numerical and econometric benchmark

models. As concerns headline inflation, simple numerical benchmarks (“rules of thumb”) may

in fact offer an alternative to more complex forecasting techniques, and can be adopted by any

economic agent at little cost. For example, the prevailing inflation rate or the central bank’s

inflation target may be used as potential forecasts. Simple econometric models, which are

“imposed” on the data, without following a particular selection procedure, are another rapid

and inexpensive way of forecasting inflation. Typically, however, forecasters also rely on

econometric models that are more complex and not as readily available. The second group of

models considered in this paper, consists of autoregressive moving average (ARMA) models

picked on the basis of a penalty function (information criterion). For the third group of

autoregressive distributed lag (ADL) models, the information set is extended to potentialexogenous predictors of inflation.

In a first step the models are applied to headline inflation to generate direct forecasts. All

models are subsequently applied separately to the five components to obtain the indirect

inflation forecasts. This method requires the specification and selection of one model per

component, thus adding a number of intermediate steps, which are not required in the direct

approach. While the advantages of indirect relative to direct forecasts are ambiguous from a

theoretical point of view (cf. section 2), indirect forecasts are attractive in practice, as they can

1

The five main components of headline inflation are energy, processed food, unprocessed food, non-energyindustrial goods and services. While this breakdown is standard, some authors (e.g. Bermingham and

D’Agostino (2010)) also study lower levels of disaggregation.



3

be associated to more detailed narratives and economic arguments, and avoid inconsistencies

between headline inflation and component-specific forecasts.2

The paper’s second objective is to assess the impact of the large swings in commodity prices

observed since 2007, and of the economic and financial crisis, on inflation forecasting. As

noted below, it emerges from the literature on inflation forecasting that the performance of amodel depends inter alia on the estimation and evaluation period. At the current juncture, it is

thus particularly interesting to assess to what extent the financial and economic crisis, which

itself was preceded by a shock in global food and commodity prices, has impacted the

performance of different models and approaches in both absolute and relative terms.

Substantial forecast revisions by international institutions and professional forecasters suggest

that the traditional approaches have indeed been seriously challenged (table A.1 in the annex

illustrates this by way of example, showing different vintages of inflation forecasts made from

2006 onwards for the years 2008 and 2009). The impact of the crisis on the relative

performance of different inflation forecasting models and methods is studied by repeating the

comparative evaluation for two different sample periods ending before and after the onset of

the crisis, respectively.

The remainder of the paper is organised as follows: after a brief review of the literature in the

next section, section 3 presents the pattern of euro area inflation developments since 1996.

Section 4 introduces the benchmark models considered, as well as the algorithms that are used

to select autoregressive and ADL-models. The evaluation of the different models in terms of

their forecast accuracy during the crisis is presented in section 5. Section 6 presents the

comparative assessment for the pre-crisis period, essentially showing how the conclusions

from section 5 would have been different, if the comparison had been performed three years

earlier. Section 7 concludes.

2. Literature review

Over the past two decades many central banks around the world have adopted inflation

targeting frameworks. Their central feature is a publicly announced quantitative inflation

target, typically expressed as a single number or a range, to be met over the medium term

(Bernanke and Mishkin, 1997; Hammond, 2011). The main objective of a pre-announced

target-level is to anchor inflation expectations and notably to prevent second-round effects in

the event of a transitory shock. If credible, it may thus contribute to keeping inflation stable

and low. An inflation target also provides a measure by which a central bank’s performance

can be judged ex post by the public: the closer the observed inflation rate and the inflationtarget are to each other, the better the central bank's track record, and the more compelling is

the incentive to trust the central bank as regards the future, by using the target as a forecast ex

ante.3

Inflation forecasts represent a key element in an inflation targeting framework. As

noted by Svensson (1997), a central bank’s control over inflation is imperfect and missing the

target may be the consequence of factors outside its command. That said, a central bank

2 It is also noteworthy that many published forecasts of headline inflation are based on an indirect approach; this

is the case notably for the Eurosystem staff’s inflation projection exercise and for European Commission

forecasts.3

The incentive is likely to be even greater, if it can be shown that the inflation target has also outperformedcompeting alternatives in the past, and adopting the inflation target as an own forecast would consequently have

constituted the optimal strategy ex ante.



4

pursuing an explicit inflation target would still set its monetary policy instrument in such a

way that its inflation forecast would coincide with the official inflation target; inflation

forecasts, which are more controllable than the inflation rate itself, hence become an implicit

intermediate target, and as such also shift into the focus of public scrutiny.

In the euro area, the Treaty assigns to monetary policy the primary objective of maintainingprice stability. While the European Central Bank (ECB) did not adopt an inflation targeting

framework as such, its Governing Council nonetheless provided a quantification of price

stability, defined as an annual increase in the HICP below, but close to 2% over the medium

term for the euro area as a whole (ECB, 2003). It hence set a reference value, serving

concurrently as a yardstick for the assessment of the ECB’s past performance, and as a point

of orientation for inflation in the future. Diron and Mojon (2005) compare the forecast

performance of inflation targets of the euro area and seven inflation targeting countries, to

model-based and published inflation forecasts respectively. They find that the central banks’

targets generally match or outperform the alternatives considered, and conclude that there are

substantial benefits in adopting the stated target as a forecast, in particular over longer

horizons.

A number of authors have shown that simple inflation forecasting models have often

performed well with respect to more elaborated ones. Fritzer et al. (2002) find that for

Austrian inflation, univariate (ARIMA) forecast models outperform multivariate (VAR)

models at short horizons; the opposite is however true at more distant horizons (8 to 12

months). Considering a set of univariate and multivariate euro area inflation forecasting

models, Hubrich (2005) testifies the good overall performance of the autoregressive model,

which even turns out to be the most accurate model at a 12-month forecast horizon. For the

US, Stock and Watson (1999) also note the “surprisingly” strong performance of

autoregressions and random walk models. Also for the US, Atkeson and Ohanian (2001)

evaluate the accuracy of Phillips curve-based inflation forecasting models based on the non-accelerating inflation rate of unemployment. They find that none of three sets of inflation

forecasts considered (forecasts published by the Federal Reserve Board, as well as two model-

based forecasts), succeeds in systematically outperforming the random walk model used by

them as benchmark.

While most economic agents’ and observers’ ultimate interest in inflation centres on the

headline rate, the question whether it should be forecasted directly (‘top-down’) or indirectly

(‘bottom-up’), has received a lot of attention among forecasters.4

Hubrich (2005) reviews

theoretical considerations behind the two approaches, noting that the “results from asymptotic

theory and small sample simulations do not give a clear answer regarding [their] relative

forecast accuracy” (p.122). In the absence of clear theoretical guidance, the judgement thusessentially becomes an empirical one. A number of authors have empirically assessed the

relative forecast performance of direct and indirect approaches to forecasting. Overall, their

findings do not allow systematically favouring one method over the other, let alone discarding

one. Indeed, the findings seem to be sensitive, inter alia, to the geographical entity, the types

of models considered, the forecast horizon, the data frequency and the transformation of the

price index series, as well as the periods chosen for model selection and evaluation. Fritzer et

al. (2002) construct two series for Austrian headline inflation by aggregating component-

specific inflation forecasts generated by ARIMA and by VAR models, respectively. In the

ARIMA case, the indirect approach generally beats the corresponding direct ARIMA

4 Another indirect way of forecasting, not considered here, would be to forecast individual Member States’ series

and to aggregate them to obtain a euro area forecast series (see Benalal et al. (2004)).



5

forecasts. In the VAR case, however, the indirect approach becomes only slightly superior at

distant horizons. Moser et al. (2004) find that indirect forecasts for Austrian inflation appear

to be somewhat more precise than the best direct inflation forecast considered; their model

competition is based on ARIMA, VAR and factor models. Den Reijer and Vlaar (2006),

considering AR, VAR and VECM models, find that for the Netherlands the indirect approach

is only superior at closer forecasting horizons (up to 7 months). For the euro area, they findthat the indirect approach outperforms the direct approach on all forecast horizons evaluated

(18 months). Meanwhile, Benalal et al. (2004), considering both univariate and multivariate

(VAR, Bayesian VAR and single equation) models, find that for the euro area (as well as for

Germany, France, Italy and Spain) the direct HICP forecasts improve upon indirect forecasts

for horizons beyond 12 months. For closer horizons their results are however less evident.

Hubrich (2005) finds that the indirect approach primes for forecasts of euro area inflation one-

month ahead, but that it does not generally improve upon direct forecasts at forecast horizons

of 6- or 12-months, which are more relevant from a policy point of view. In a more recent

study, Bermingham and D’Agostino (2010) find that aggregating forecasts of inflation

components (at different levels of disaggregation) yields more accurate forecast than direct

forecasting for both the euro area and US inflation. However, they stress the necessity of specifying an appropriate model for each individual component first.

3. Euro area inflation between 1996 and 2010

3.1 ANNUAL INFLATION PATTERNS

This section provides a brief description of euro area (16 Member States) inflation

developments between 1996:01 and 2010:12.

5

Figure A.1 in the annex displays the price levelindex (in logarithmic transformation), as well as monthly and annual changes respectively for

all series. Annual headline inflation, measured by year-on-year changes in the overall

harmonised index of consumer prices (HICP), has averaged around 1.9% over the sample

period. It steadily declined from 1997 until the introduction of the euro in 1999. It then

rebounded and remained broadly stable between the early 2000's and mid-2007, hovering in a

range of 1.6% to 3.1%. In the following period and until the end of the sample, inflation was

characterised by large swings: it climbed to 4.0% in July 2008, plunged to -0.6% one year

later and progressively returned to around 2% by the end of the sample period. These swings

were primarily the result of the patterns of global commodity prices, which impacted directly

on food and energy inflation in the euro area during that period, and coincided with the "great

recession" period triggered by the financial crisis that started in mid-2007 and intensified afterthe failure of Lehman Brothers in September 2008.

A notable feature of annual euro area inflation developments is that price indices in the

different categories have on average grown at a very different speed in the period considered

(see table 1). The non-energy industrial goods component, which on average has accounted

for almost one third of the consumer basket, is the only category for which prices have grown

at an average pace below 2% a year (0.8%). Low inflation in this category most likely reflects

the strong external competitive pressures that exist for many manufactured products, as well

as quality improvements in the product items covered. At the other extreme, with an average

of 4.0% a year, energy prices have grown fastest over the period considered, followed by

5The HICP indices are published by Eurostat.



6

processed food (2.4%) and services (2.2%). Energy inflation has also been the most volatile,

with year-on-year rates falling into a 31 percentage point-range, from a high of 17.0% (July

2008) to a low of -14.2% (July 2009). Unprocessed, and to a lesser extent processed food

inflation, also oscillated considerably. Annual inflation of services and non-energy industrial

goods respectively has evolved in a smoother way, thus lessening the volatility of overall

inflation. Services and processed food are the only components which never experiencednegative annual price growth, having fallen to respective minima of 1.2% and 0.4%. It is also

confirmed that inflation in the core categories – non-energy industrial goods, services and to a

lesser extent processed food – generally fluctuates less and within narrower bands. Finally, it

is noteworthy that for most components the extreme values in annual inflation occurred after

2007.

Tab le 1: Desc rip tive sta tistics of euro a rea inflat ion (1996:01-2010:12)6

cp00 enrgy foodproc foodunp igoodsxe serv

Mean 1.93 4.03 2.37 2.14 0.76 2.23

Median 2.01 3.33 1.96 1.98 0.76 2.35

Maximum 4.06 17.01 7.20 8.93 1.78 3.35

Minimum -0.65 -14.25 0.35 -1.65 -0.12 1.18

Range 4.70 31.26 6.85 10.57 1.90 2.17

Std Dev 0.77 6.44 1.46 2.18 0.35 0.52


Mean 0.16 0.34 0.19 0.18 0.08 0.18

Median 0.18 0.30 0.13 0.16 0.13 0.14

Maximum 1.11 4.10 1.18 3.47 2.48 1.14

Minimum -0.83 -4.90 -0.12 -1.59 -3.14 -0.75

Range 1.94 8.99 1.31 5.06 5.62 1.89

Std Dev 0.29 1.44 0.22 0.73 0.89 0.37

Annual inflation (%)

Monthly inflation (%)

Source: own calculations based on Eurostat

3.2 INTRA-YEAR VARIATION OF INFLATION

Some of the inflation series, in particular non-energy industrial goods and services, display

clear seasonal patterns, which shape the profile of monthly headline inflation in proportion to

their weight in the HICP. The additional presence of seasonal trends in some of the series also

generates a seasonal pattern in annual inflation.

Figure 1 below (left panel) shows the average monthly profile for overall inflation over the

sample period (applying the 2010 weights). Monthly headline HICP inflation is positive in

most months (+0.16% on average). Notable exceptions are the sales months January and July,

when prices have declined on average by 0.32% and 0.14% percent, respectively. Both drops

in the price level offset increases of a similar magnitude in the preceding months, i.e.

December (+0.31%) and June (+0.10%), respectively. About two thirds of the annual price

increases occur in the first half of the year, with March (+0.54%), April (+0.34%) and

February (+0.31%) typically being the months with the strongest price increases.

6Note that one observation is lost compute monthly inflation and 12 are lost to compute annual inflation.



7

Figure 1: Breakdown of intra-year inflation profile and contributions to annual inflation

Typical inflation Profile(Based on 1996:01-2010:12 averages and 2010 weights)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Energy Foodunp Foodproc NEIG Services HICP

Euro Area headline inflation and contribution(Based on 1997:01-2010:12)

-2

-1

0

1

2

3

4

5

Jan-97 Jan-99 Jan-01 Jan-03 Jan-05 Jan-07 Jan-09

Non-ene rgy ind . goods E ne rgy

Services Unprocessed food

Processed food Headline HICP Source: own calculations based on Eurostat

The seasonal plots of monthly inflation for the five components (figure A.2 in the annex)

provide additional insights regarding intra-year variation. A seasonal profile is only hardly

discernible for energy inflation. Processed food prices typically make a jump in January,

which is likely to reflect the scarcity (or unavailability) at that time of the year of certain itemsincluded in the index. However, intra-year variation is very low otherwise. In contrast,

unprocessed food displays a very pronounced seasonal pattern. Similar to processed food,

prices for unprocessed food make a distinctive leap in January, but decline from June to

August. The high volatility of monthly inflation can also result from disruptions such as

weather-related uncertainties of crop production or animal and vegetal diseases. Non-energy

industrial goods prices exhibit the most pronounced seasonal profile, with significant price

drops in the sales months January and July. Two interesting developments are worth pointing

out: first, monthly price decreases in January and July have become larger over time, while,

secondly, the price increases which have followed in March, and in September and October,

respectively, have accelerated over the years. This suggests that summer and winter sales may

have become more aggressive over time, with firms offering increasingly large discounts,while the following rebound in prices has also become stronger. Services inflation also

displays a quite marked intra-year variation, inter alia determined by holiday periods.

4. Model selection strategy

This section sets out the detailed strategies that are followed to select the models, which will

ultimately be evaluated on the basis of their forecast precision. The first sub-section (4.1)

introduces the benchmark models; the ARMA and ADL-model selection algorithms are

presented in sub-sections 4.2 and 4.3, respectively. All model selection procedures are appliedto the headline inflation series for the specification of direct inflation forecasting models.

Separately, they are applied to each of the five inflation component series to specify the

component-specific models which are the basis of the indirect inflation forecasts.

4.1 RULES OF THUMB AND ECONOMETRIC BENCHMARK MODELS

To obtain a yardstick for judging the forecasting accuracy of candidate models, a group of six

benchmark models is considered. It contains four econometric models, including three

autoregressive models - AR (1), ARMA (1,1) and AR (12) – and a seasonal average model,

setting monthly inflation in a particular month equal to the average inflation observed in thatmonth in the past. For headline inflation, two additional "rules of thumb" are considered: the



8

first is the ECB’s definition of price stability, discussed in the survey. For the purpose of this

paper, and following Diron and Mojon (2005), the ECB’s inflation objective is defined as an

annual inflation rate of 1.9% (denoted “ECB-target” in the following). Since the objective of

price stability applies to the medium-term, the target should be expected to improve relative

to other models as the length of the forecast horizon increases. Target misses at close forecast

horizons should accordingly not be ascribed to central bank decisions, as monetary policy hasno corrective impact on inflation in the very short-run. The second rule of thumb ("naïve"

model) simply corresponds to the year-on-year inflation rate prevailing at the moment the

forecast is made; it hence does not take account of temporary factors that may explain the

current inflation rate. Nevertheless, the “model” is easy to implement, as it only requires

knowledge of current inflation, and also recognises that the last available observation

generally constitutes a natural starting point and orientation for any forecast. The naïve

approach could even be expected to perform reasonably well at short horizons when there is

inflation persistence or at more distant ones when the last available inflation rate is already

close to target.

4.2 ARMA-MODEL SELECTION ALGORITHM

Autoregressive forecasting models rely on identifying the data-generating process (DGP)

underlying the inflation series. This “essentially agnostic” (Meyler et al. (1998)) way of

forecasting is purely mechanical rather than fundamentals-based, and can therefore in some

ways be criticised as simplistic. Nonetheless, univariate models have often been found to

perform well in short-run inflation-forecasting (see survey), and have the practical advantage

that data requirements are limited to the series of interest.

The atheoretical nature of univariate models leaves many liberties when specifying a forecast

model. This, however, risks making the selection somewhat arbitrary and non-transparent.Applying a Box-Jenkins model-selection approach could indeed lead to find models with a

higher (in-sample and out-of-sample) fit, but would also introduce a large scope of discretion,

resulting in different models depending on the individual forecaster (see Meyler et al. (1998)

for a discussion). For that reason, it is proposed to pick the models retained for the evaluation

stage through an automated selection procedure based on objective selection (information)

criteria (cf. Meyler et al. (1998), and Hubrich (2005)). Information criteria essentially differ in

the severity by which they sanction the inclusion of additional parameters in a model, relative

to its fit. Of the two mainly used criteria – Schwarz (SIC) and Akaike (AIC) – the SIC

generally leads to more parsimonious lag orders, while the AIC tends to overfit a model by

putting a lower penalty on additional parameters than the SIC (for a discussion see Lütkepohl

and Krätzig (2004)). In this paper, a large set of autoregressive models are estimated. Thosewith the lowest AIC and the lowest SIC, respectively, are retained and carried forward to the

out-of-sample simulation exercise.

The order of an autoregressive integrated moving average (ARIMA) process is expressed as

(p, d, q)7, where p refers to the number of lags of the dependent variable and q to the number

of moving average (MA) terms, and d is the order of integration of the original series. While p and q will be determined by the minimum value of the information criterion, the differencing

decision is made on the basis of a separate stationarity analysis. The latter, presented in annex

2, has suggested using either the first-differenced series (i.e. monthly inflation)8

or seasonal

7 Seasonal lags and MA terms are not considered here.8 The unit root hypothesis is rejected for all first-differenced series by the Philips-Perron test. The ADF-test leads



9

differences of first-differenced series, for all series. For the present exercise, the first-

differenced log series (monthly inflation) is used, i.e. d=1; this is also in line with other

authors (e.g. Hubrich, 2005). Since monthly inflation now is the series of interest, the notation

ARMA (p, q) will be used in the following.

Four ARMA-specifications are considered. The first sample observation in first-differencedform is 1996:02 and 12 pre-sample observations have to be set aside to allow for a maximum

of 12 lags, while ensuring an equal number of observations across all estimations. The models

are hence estimated over the samples 1997:02-2010:12 (including the crisis) and 1997:02-

2007:12 (pre-crisis), respectively. The basic ARMA specification is given by

(U.1) t t L Bc L A e m )()( += ,

where p

p L L L A a a ---= L11)( and q

q L L L B b b ---= L11)( , with 11max= p and

11max=q , and µ t is the first difference of the log price index series under consideration (i.e.

monthly inflation). L is the lag-operator. The selection procedure considers only full sets of adjacent lags (i.e. including all lags up to the maximum). Determining p and q requires the

estimation of 144 ((p+1)*(q+1)) models for a given selection criterion. Note that pure AR

(i.e. q=0) and pure MA (i.e. p=0) models are special cases that are considered under this

selection procedure. The second specification, which is obtained by augmenting specification

(U.1) by a full set of seasonal dummies (SD)9, is likely to be particularly relevant for series

exhibiting a distinct intra-year pattern. It is expressed as:

(U.2) t d d t L BSDc L A e d m )()(

11

1++= å

As inflation in a particular month may be affected by monthly inflation one year earlier and

may be driven by seasonal regularities, specification (U.1) is augmented by the twelfth lag of

monthly inflation, becoming

(U.3)t t L Bc L A e m )()(12

+= ,

where 12

121

12 1)( L L L L A p

p a a a ----= L , with 11max= p , and B(L) is defined as above.

The twelfth lag of the dependent variable is thus explicitly introduced in the regressions,

while the choice of p and q is again left to the information criterion. This ARMA "with a

hole" is a special case of a (12, q) process, possibly with some intermediate lag coefficients

set to zero. A pure AR (12) process is thus also part of the specifications considered. In

analogy with specification (U.1), (U.3) is augmented by seasonal dummies, yielding thefollowing specification:

(U.4) t d d t L BSDc L A e d m )()(11

1

12 ++= å

The order of the processes eventually retained by the algorithm is shown in the tables A.6-

A.12 in annex 5.

to more ambiguous results.9 SD is equal to 1 in month d and equal to 0 otherwise. As the equation includes a constant, 11 seasonal dummies

are included.



10

4.3 AUTO-REGRESSIVE DISTRIBUTED LAG MODELS

The third group of models exploits structural relationships observed in historical data between

inflation and different exogenous variables. These models can be broadly categorised,

according the type of exogenous variable included, as cost-push (supply-side) or demand-side

models.10

The former include cost-indicators as potential drivers of inflation and dependmainly on vertical production relations (e.g. energy prices strongly depend on oil prices). The

latter are essentially Philips-curve-type relationships, which explain inflation by (deviations

in) measures of actual or potential economic activity (e.g. output gap, unemployment,

industrial production): low demand leads to excess supply and, as firms need to liquidate their

products, to lower pricing power and eventually lower prices – and vice versa. Finally, other

variables, such as household surveys, may also exhibit leading indicator properties for

inflation.

4.3.1 INVESTIGATION OF "RELEVANCE" OF EXOGENOUS VARIABLES

Following Fritzer et al. (2002), an exploratory analysis is performed first, aiming to identifythe most relevant exogenous variables among a set of candidates. The selected variables will

enter the more refined ADL model-selection process described in the next sub-section.

A total of around 40 exogenous variables are considered here that are of monthly frequency

(i.e. no interpolated quarterly data are used), and can be classified in the following broad

categories, which can all be expected to drive inflation and/or act as leading indicators:

commodity prices; exchange rate; industrial production; industrial orders; surveys; labour

market . The individual series are listed in table A.4 (annex 3).

The following “pre-fitting” equations are estimated for the sample period 1997:02 to 2010:12:

(B.0)t

j

jk t i

i

j

it i

j

t xc e b m f m +++= åå=

--

=

--

12

0

12

0

1 ,

where the j superscript identifies the inflation series and x is the exogenous variable of

interest, which in general enters the equation as first-difference of the log-series (for some

series the percentage or absolute change is retained). Each equation is estimated for three

different displacements (k=1, 6, 12) of the exogenous variable, to assess whether it could

constitute a leading indicator for inflation. A contemporaneous equation (with no

displacement, i.e. k=0) is also fitted, as a feedback effect from inflation to the exogenous

variables used here can be ruled out on conceptual grounds and as such should not give rise to

endogeneity concerns. The joint significance of the exogenous variables is tested applying an

F-test. Under the null hypothesis it assumes that the coefficients on the exogenous variables

(the betas) are jointly equal to zero, such that the equation (B.0) reduces to an AR(12) model.

Table A.5 in the annex 3 reports the F-statistic and the probability value, as well as the

goodness of fit of the unrestricted specification, measured by the adjusted coefficient of

determination. For headline inflation the pre-fitting equations suggest that commodity prices

10 Monetary models are another category of models (not considered in this paper; see for example Hofmann,

(2006)), which could be used for longer horizons and rest on the idea that money is neutral in the long run,

following the Friedman-Schwarz insight that ‘inflation is always and everywhere a monetary phenomenon’. Therelationship between monetary growth and inflation has also shaped the Eurosystem’s monetary policy strategy,

in which monetary analysis constitutes the second of two pillars (ECB, 2003).



11

and activity variables (industrial production, orders and employment) are a priori relevant

leading indicators and significantly improve the fit of the regressions, contrary to exchange

rates and consumer surveys (with the exception of expected price trends over the next 12

months).11

On the basis of this pre-fitting analysis, the significant exogenous variables, which offer thelargest explanatory potential, are carried forward to the actual ADL-model selection. Some

variables that are considered particularly important from either a macroeconomic (e.g.

commodity prices, exchange rates) or sectoral (e.g. agricultural raw materials in the case of

food inflation) perspective, are maintained regardless of this pre-fitting outcome.

4.3.2 ADL-MODEL SELECTION-ALGORITHM

This section describes the selection procedure for ADL-models. The estimated process in its

most general form is given by the following ADL-model:

(B.1) t

q

j

jt j

p

i

jit i

jt xc e b m f m +++= åå

=

-

=

--

00

1 ,

with pmax

=11 and qmax

=25, allowing for a lead time of two years; µ and x are defined as in the

pre-fitting equation (B.0) above, except that the lag orders p and q are now determined via the

penalty function. Adding a full set of seasonal dummies to specification (B.1) yields the

following equation:

(B.2) t

q

j

jt j

p

i

j

it id

j

t xSDc e b m f d m ++++= ååå=

-

=

--

00

1

11

1,

The next specification modifies (B.1) by adding the twelfth lag of the dependent variable into

the equation:

(B.3)t

q

j

jt j

j

t

p

i

j

it i

j

t xc e b m m f m ++++= åå=

--

=

--

0

12

0

1

Augmenting it by a set of seasonal dummies, yields the following equation:

(B.4)t

q

j

jt j

j

t

p

i

j

it id

j

t xSDc e b m m f d m +++++= ååå=

--

=

--

0

12

0

1

11

1

For each inflation series and for each respective exogenous variable, the model is estimated

for all combinations of p and q up to their respective maximum, yielding a total of 312

(12*26) models per specification, including a set of pure AR models (i.e. no exogenous

variable) and a set of pure distributed lag models (i.e. no lag dependent variable) as special

cases. The combination of p and q returning the lowest information criterion is retained for

the evaluation stage. The AIC is now used as evaluating criterion, as it imposes a lower

penalty on additional variables than the SIC, and thus reduces the probability of dropping the

exogenous variable.

11An analogous exercise is performed for the five inflation components (available upon request).



12

Following the strategy described in section 4.2 (ARMA) and 4.3 (ADL) above, carries the

risk that a good forecast model is already discarded at the selection stage. To avoid this, all

candidate models initially considered could in principle be directly evaluated on their

forecasting accuracy - which after all is the ultimate feature of interest - without undergoing

this pre-selection stage. However, there are two good reasons to maintain a pre-selection:

first, it ensures that the set of candidate models is narrowed down to a more manageable size.Secondly, it screens models according to their fit, ensuring that a meaningful statistical

relationship exists between the variables.

5. Evaluation of the forecast accuracy during thecrisis

The candidate models picked by the algorithms are evaluated by their out-of-sample accuracy

measured by the recursive Root Mean Squared Forecast Error (RMSFE) presented in annex 4.

Each forecast horizon is evaluated over 48 observations, i.e. 4 years. The first recursive model

is estimated over the sample 1997:02 to 2005:07. The end date of the sample is gradually

extended until 2009:06, leaving 18 remaining observations for evaluation purposes.12

Overall,

the evaluation period was relatively calm until the end of 2007, but became more agitated

afterwards, when global oil and food prices started to hike and the financial crisis started.

Headline inflation between 2005:08 and 2010:12 averaged 1.94%, i.e. close to target, but was

very volatile (see table A.2.1 in annex 1 for descriptive statistics of the evaluation period).

5.1 DIRECT FORECASTS OF HEADLINE INFLATION DURING THE CRISIS

Table 2 (left panel) below summarises the accuracy of the main model groups, displayingtheir average RMSFEs over all 18 forecast horizons, as well as the average RMSFEs for three

blocks of six-month forecast horizons. Table A.6 in annex 5 displays the RMSFEs for each of

the 18 forecast horizons for all competing headline inflation models. The ADL-model

specification (i.e. B.1-B.4) included in the table, is the one yielding the lowest average

RMSFE.13

12One-step-ahead forecasts are thus evaluated over the period 2005:08 to 2009:07, while the 18-step-ahead

forecasts are assessed over the 48-month period between 2007:01 and 2010:12.13 When evaluating ADL models, a path for the exogenous variables needs to be specified. In this paper the out-

of-sample evaluations of the ADL models are based on conditioning assumptions that correspond to the true path

of the exogenous variable of interest. While this assumption of perfect foresight is of course very strong and

unlikely to be met in practice, it however allows focussing on the particular exogenous variables. With

assumption errors thus effectively being ruled out as a source of inflation forecast error, the RMSFEs obtainedshould be regarded as a lower bound and an indication of the margin of improvement for other models. The

results may hence help to focus on those variables that are particularly valuable as inflation predictors.



13

Tab le 2: Averag e RMSFEs of ma in model c a tegories in crisis-sample (summary)

Horizon: 1 to 6 7 to 12 13 to 18 1 to 18 1 to 6 7 to 12 13 to 18 1 to 18

Benchmarks

ECB 1,12 1,19 1,19 1,17 (-) (-) (-) (-)

Naive 0,77 1,60 1,88 1,42 (-) (-) (-) (-)

AR(1) 0,71 1,17 1,24 1,04 0,71 1,17 1,24 1,04ARMA(1,1) 0,69 1,15 1,21 1,02 0,70 1,16 1,24 1,03

AR(12) 0,79 1,51 1,67 1,32 0,60 1,26 1,48 1,12

Seas. Dummies 0,57 1,09 1,23 0,96 0,57 1,09 1,23 0,97

ARMA (*)

Identical DGP 0,58 1,11 1,26 0,98 0,54 1,11 1,31 0,99

Component-specific DGP (-) (-) (-) (-) 0,48 1,02 1,20 0,90

ADL (oilusd) (*)

Identical model 0,35 0,75 0,95 0,68 0,33 0,70 0,89 0,64

Component-specific model (-) (-) (-) (-) 0,32 0,67 0,86 0,62

Combination (-) (-) (-) (-) 0,28 0,46 0,53 0,42

Direct forecast Indirect forecast

Note: (*) Refers to the model specification generating the lowest RMSFE of the respective model group

For headline inflation, the accuracy of forecasts produced by the ARMA-models selected by

an information criterion tends to be comparable to that of benchmark models. In particular,

the seasonal dummy-model appears difficult to beat, reflecting the importance of the intra-

year inflation pattern. The ECB-target improves in relative terms with the distance of the

forecast horizon, dominating all ARMA-models on horizons beyond twelve months, which

are more relevant from a monetary policy perspective. The naïve model is rapidly

outperformed by the ARMA-models, which is unsurprising in the light of the swings in

inflation observed during the evaluation period. Considering ADL-models reveals that theinclusion of commodity prices, in particular of oil prices, considerably reduces the forecast

errors over all horizons compared to ARMA and benchmark models. The RMSFE of the

model including dollar-denominated oil prices corresponds to around 70% of that of the

seasonal-dummy model and to around 60% of the static ECB-target forecast. Industrial

production, industrial orders and labour market data also improve the out-of-sample fit, albeit

to a lesser extent.

5.2 INDIRECT FORECASTS OF HEADLINE INFLATION DURING THE

CRISIS

Indirect headline inflation forecasts are obtained by aggregating forecasts of each of the five

components (generated by some component-specific models), weighted by their share in the

HICP in the relevant year. The aggregated inflation series obtained through this indirect

approach are then also evaluated by the RMSFE. While a large number of combinations of

component-forecasts are possible, six sets of aggregation are considered here: i) aggregations

of forecasts produced by the four econometric benchmark models; ii) an aggregation of

forecasts obtained by imposing the data-generation process of the most accurate direct

ARMA-model on all series; iii) an aggregation of ARMA forecasts, allowing for a

component-specific data-generation processes; iv) an aggregation of ADL-forecasts using

dollar-denominated oil prices as an explanatory variable for all components, imposing the

same model on all series; v) an aggregation of ADL-forecasts based on dollar-denominatedoil prices, now allowing for component-specific specifications; vi) an aggregation of those



14

forecasts, which have given rise to the lowest average RMSFE for each component, i.e.

allowing for component-specific models with different exogenous variables. Aggregations i),

ii) and iv) thus fit an identical model to each individual series, as to the headline series; the

other aggregations consider true component-specific models.

Before turning to the evaluation of the aggregated series, the results of the forecasting modelsfor the individual inflation components are briefly commented in this paragraph. The

candidate models for the respective components and their average RMSFEs over all 18

forecast period, and the average RMSFEs over three blocks of six-month horizons are

reported in tables A.8 to A.12 in the annex. The results show that the components attributed to

core inflation, which are less volatile and exhibit stronger regularities, also have the highest

out-of-sample fit. This is well-illustrated by the non-energy industrial goods and services

series on the one hand, which have the smallest forecast errors, and by the energy series on

the other, which has the largest. In the case of energy inflation, the highest forecast accuracy –

albeit low by the standards of the other components – is achieved by an ADL-model that

includes oil prices.14

For processed food inflation, the ADL-model including the euro-dollar

exchange rate produces the smallest forecast errors.15

For unprocessed food inflation, thehighest forecast accuracy is obtained by including activity variables and industrial order data,

which dominate commodity prices, such as agricultural raw materials and cereals. The strong

seasonal regularities observed for non-energy industrial goods inflation generally facilitate

the forecasting of this series, as is confirmed by the generally low RMSFEs relative to other

inflation series. Adding exogenous variables can in some cases (e.g. industrial production or

labour market variables) reduce the forecast errors even further, albeit only marginally. For

services inflation, the forecast accuracy of the simple seasonal-dummy model is similar to that

of the best ARMA-models picked by the algorithm. An ADL-model that includes the

unemployment rate slightly improves the out-of-sample fit with respect to benchmarks and

ARMA-models.

The RMSFEs obtained by the indirect approach are reported in table 2 (right panel) and in

more detail at the bottom of table A.6 in the annex. Except for the AR (12) model, indirect

forecasts based on benchmark models do not yield better forecasts than the corresponding

direct forecast. The indirect forecast obtained from applying the DGP of the best direct model

to all component-series, does not improve upon the direct forecast overall: while the forecast

accuracy is slightly higher up to six-months ahead, it deteriorates over horizons further than

12 months away. In contrast, when allowing for differentiated component-specific DGPs, the

indirect approach clearly outperforms the best direct ARMA-model. This supports the

conclusion of Bermingham and D’Agostino (2010), who stress the importance of specifying

an appropriate model for each component. Indirect forecast resulting from ADL-models

including oil prices dominate the corresponding direct approach, regardless of whether anidentical model is imposed or component-specific models are fitted. The final aggregation,

which is effectively a multivariate forecasting set-up, relies on dollar-denominated oil prices

(energy), the exchange rate (processed food), industrial production of consumer goods

(unprocessed food and non-energy industrial goods) and the unemployment rate (services). It

generates a lower average RMSFE than all direct and indirect approaches considered: the

average RMSFE corresponds to 36% of that of the ECB-target and 30% of that of the naïve

14Interestingly, dollar-denominated oil prices constitute a better predictor for energy inflation in the euro area

than euro-denominated oil prices (the same holds for headline inflation).15

It is also worth noting that the agricultural raw materials price index is not retained by the ADL algorithm.While the unprocessed food price index is retained by the algorithm, the resulting model does not yield better

forecasts.



15

model. Relative to the best direct forecast (ADL-model including dollar-denominated oil

prices), the average RMSFE corresponds to 63%. This aggregation also improves in relative

terms with the length of the forecast horizon: while for the six months ahead, the average

RMSFE of the indirect approach represents around 80% of that of the best direct model, it

drops to around 56% on horizons that are between 13 and 18 months ahead.

6. Evaluation of the forecast accuracy before theeconomic and financial crisis

The evaluation period in section 5 has to a large extent coincided with the financial and

economic crisis. As the latter is likely to have impacted the conclusions, the validity and

robustness of the latter for other periods may thus a priori be questioned. Indeed, the largeswings in global oil and food prices after 2007 and the disruptions in economic activity

caused by the crisis itself had a major impact on the euro area inflation profile, as illustrated

in section 3, but also on private and public institutions’ forecasts, which had to be

significantly revised (cf. table A.1). To assess the robustness of the results over time, this

section considers how the forecasting performance of the models considered above would

have been different – in both absolute and relative terms – if the selection and evaluation

process had been carried out before the start of the crisis.

To assess the pre-crisis forecasting accuracy, the last three years of the sample are dropped,

and the model selection algorithms described in section 4 are run over the sample 1997:02 to

2007:12. Maintaining an evaluation period of 48 months, the first recursive sample ends in

2002:07, while the last sample runs until 2006:06.16

While average headline inflation between

2002:08 and 2007:12 was on average somewhat higher than during the evaluation period

considered in section 5, namely at 2.17%, the volatility, measured by the range or the standard

deviation, was considerably lower (see table A.2.2 in the annex). On average, inflation in all

categories with the exception of energy was higher in the pre-crisis evaluation period.

Meanwhile, inflation volatility was lower for all components, except for unprocessed food

and non-energy industrial goods inflation.

6.1 DIRECT FORECASTS OF HEADLINE INFLATION PRE-CRISIS

Table 3 (left panel) summarises the performance of the main model groups, showing their

average RMSFEs for the entire evaluation period and for three six-month periods. Table A.7

in the annex displays the pre-crisis RMSFEs of the benchmarks and all selected directheadline inflation models. The ADL-models reported in the table correspond to the

specification (B.1-B.4) that yielded the lowest average RMSFE. The precise specifications of

the models evaluated before the crisis are consequently not necessarily the same as the ones

evaluated during the crisis.17

16One-month ahead forecasts are assessed over the period 2002:08 to 2006:07, while the 18-month forecast

horizon is evaluated over the period 2004:01 to 2007:12.17

It is noteworthy that some exogenous variables may be retained by the algorithm in one period, but not in theother. In the case of processed food inflation for example, agricultural raw materials prices would have been

included in an ADL-model prior to the crisis, but not thereafter.



16

Tab le 3: Ave rag e RMSFEs of m a in model c a tegories in pre-c risis-samp le (summary)


Benchmarks

ECB 0,34 0,32 0,34 0,33 (-) (-) (-) (-)

Naive 0,29 0,36 0,36 0,34 (-) (-) (-) (-)

AR(1) 0,44 0,52 0,39 0,45 0,47 0,55 0,38 0,47 ARMA(1,1) 0,42 0,49 0,38 0,43 0,47 0,55 0,32 0,45

AR(12) 0,31 0,35 0,35 0,34 0,29 0,35 0,33 0,32

Seas. Dummies 0,30 0,40 0,42 0,37 0,31 0,40 0,40 0,37

ARMA (*)

Identical DGP 0,28 0,35 0,37 0,33 0,30 0,48 0,55 0,44


ADL (oilusd) (*)

Identical model 0,22 0,26 0,23 0,24 0,22 0,30 0,31 0,28


Combination (-) (-) (-) (-) 0,20 0,23 0,25 0,23



Comparing the forecast accuracy of the different models highlights the relatively strong

performance of the ECB-target. On average it dominates all benchmark and ARMA-models,

essentially due to its good performance over horizons beyond 8 months. It is also interesting

to note that, contrary to other models, the forecast errors of the ECB-target remain stable and

even decline with the length of the f orecast horizon, consistent with the medium-term

character of the price stability objective.18

Finally, the ECB-target also performs reasonably

well compared to ADL-models, in particular at more distant forecasting horizons. The

average RMSFE of the best direct model, an ADL-model including oil prices, corresponds to72% of the ECB-targets’ RMSFE. Overall, this would have supported the conclusion of Diron

and Mojon (2005) that the ECB-target constitutes a good rule of thumb over medium-term

horizons. In general, the performance of the other benchmark models was also relatively

strong compared to ARMA and ADL-models selected on the basis of the penalty function.

The naive model, for example, performed comparatively well at horizons below 12 months,

owing to the stability of inflation during that period. These results corroborate the conclusions

of other studies (cf. survey) stressing the good performance of simple inflation forecasting

models.

6.2 INDIRECT FORECASTS OF HEADLINE INFLATION PRE-CRISIS

Indirect forecasts for the pre-crisis period are obtained from the same six aggregation sets as

in section 5.2; their RMSFEs are displayed in table 3 (right panel) and in more detail at the

bottom of table A.7 in the annex.19

Again, the indirect forecasts produced by the benchmark

models cannot outperform their corresponding direct equivalent. Also in line with the results

of the crisis period, the ARMA-based indirect approach leads to lower forecast errors than the

direct equivalent, on the condition that component-specific DGPs are allowed. In contrast to

the crisis period, indirect forecasts based on ADL-models including oil prices cannot

18 The rise in the RMSFE for forecasts beyond 16 months can essentially be attributed to the strong pick-up in

inflation at the end of the sample in 2007, which does not impact on the evaluation of closer forecast horizons.19 The evaluations of the forecasting models for the individual inflation components are reported in tables A.8 to

A.12 in the annex.



17

outperform their direct equivalent. Imposing an identical model on all components actually

increases the size of the forecast errors with respect to the direct approach, while the

aggregation of forecasts of component-specific models produces comparable results to those

of the direct model.

The indirect inflation forecast obtained from the best component-specific models, allowingfor the inclusion of exogenous variables,

20yields an average RMSFE that is only marginally

below that of the best direct model. The better performance of the indirect inflation forecast is

essentially due to the better performance for horizons up to 12 months ahead. It should also be

considered in the light of the strong underlying assumptions: in particular, it requires the

knowledge of the path of three exogenous variables, while the best direct approach “only”

requires the knowledge of oil prices. The aggregation of the best component-specific forecasts

outperforms the rules of thumb (ECB-target and naïve), but by a narrower margin than during

the crisis: the average RMSFE is about 70% of that of the numerical benchmarks.

6.3

HOW DID THE CRISIS AFFECT THE ABSOLUTE AND RELATIVEFORECASTING ACCURACY?

Table 4 reports the ratio of the pre-crisis average RMSFE to the crisis average RMSFE for

comparable models. A value below 100% indicates that forecast errors of the given model

group were lower before the start of the crisis. Comparing the forecast accuracy of the

different groups of direct and indirect headline inflation models in both evaluation periods

reveals that all of them have deteriorated after the outbreak of the crisis, confirming the

impression that inflation forecasting has in general become more difficult in that period. This

is particularly well-illustrated by the rules of thumb and the benchmark models whose

precision significantly worsened: for example, the average RMSFE of the naïve model rose

from 0.34 before the crisis to 1.42, implying that taking the current inflation rate as aninflation forecast yielded four times larger errors with the crisis. The ECB-target forecast also

worsened significantly with the crisis, as the average RMSFE increased from 0.33 to 1.17.

20

Dollar-denominated oil prices (energy and non-energy industrial goods); exchange rate (processed food); euro-denominated oil prices (unprocessed food); services inflation is best modelled by an ARMA models including

seasonal dummies.



18

Tab le 4: Pre-c risis ave rage RMSFEs rela tive to c risis ave rage RMSFEs (in %)


Benchmarks

ECB 29,9 26,7 28,4 28,3 (-) (-) (-) (-)

Naive 37,5 22,4 19,3 23,8 (-) (-) (-) (-)

AR(1) 62,6 44,1 31,8 43,4 66,3 46,9 30,8 44,9ARMA(1,1) 61,1 42,3 31,1 42,1 67,6 47,3 25,7 43,2

AR(12) 39,1 23,0 21,0 25,4 47,8 27,9 22,4 29,0

Seas. Dummies 52,7 36,3 34,3 38,7 54,6 36,5 32,8 38,5

ARMA (*)

Identical DGP 48,3 31,2 28,9 33,6 55,0 43,0 42,2 44,8


ADL (oilusd) (*)

Identical model 61,3 34,6 24,8 34,7 66,7 42,9 34,8 43,3


Combination (-) (-) (-) (-) 72,2 49,1 46,6 53,1



Compared to the benchmark models the weakening of more sophisticated models (i.e. ADL

and aggregations) has been relatively contained; as a consequence the rewards from investing

in them, rather than relying on simple models have increased. Put the other way round, the

attractiveness of resorting to simple rules of thumb has fallen with the crisis: evaluated during

the crisis, the average RMSFE of the dollar-denominated oil-price ADL-model (based on the

assumption of perfect foresight of the path of the exogenous variable), accounted for 59% of

the RMFSE of the ECB-target model. Before the crisis, the corresponding value was 72%.

Relative to the average RMSFE of the naïve model, the RMSFE of the oil-price ADL-modeldeclined from 70% before the crisis to 48% during the crisis. Note that the relative worsening

of benchmarks is not a consequence of the average inflation level during the two respective

evaluation periods (it was further away from the ECB-target in the pre-crisis period), but of

the more irregular inflation profile.

A look at the forecasts for the individual inflation components confirms that the deterioration

of forecasting models was broad-based, and not limited to one particular component (see

tables A.8-A.12). While in the case of energy inflation, the accuracy of the ADL-model

including dollar-denominated oil prices only deteriorated marginally with the crisis, for

processed food , all model groups produced substantially lower average RMSFEs before the

crisis. This is not surprising, given that this category was particularly affected by the globalfood price shock starting in 2007. For unprocessed food , the results are mixed: ADL-models

including oil and energy variables performed best before the crisis, while models that include

activity variables produced more accurate forecasts during the crisis. Services inflation

forecasting models have also deteriorated, regardless of the model category. For non-energy

industrial goods inflation, ARMA-models actually generated more accurate forecasts during

the crisis.



19

7. Conclusion

This paper has analysed how the financial and economic crisis has affected inflation

forecasting in the euro area. Specifically, three groups of inflation forecasting models (rules

of thumb and benchmark models; autoregressive moving average models; autoregressive

distributed lag models) were evaluated under two distinct forecasting approaches: under the

first one, the models were applied directly to headline inflation, while under the second one,

component-specific forecasts were generated first and subsequently aggregated to obtain an

indirect forecast of headline inflation.

The paper’s first objective has been to compare the accuracy of different inflation forecasting

models. Regarding the direct ones, it finds that ARMA-models determined via a penalty

function generally perform at least as well as econometric benchmark models or rules of

thumb. Adding exogenous explanatory data in an ADL-setting in many cases improves the

forecast precision further. The best direct forecasts are obtained when including oil prices,

which play a key role in explaining and predicting inflation. The gains obtained from relying

on ADL-models are particularly large during the crisis period. As far as the indirect approach

is concerned, the forecasts are generally at least as accurate as those generated by the direct

method. However, the magnitude of the gains depends much on what precisely is being

aggregated: indeed, it is only once appropriate specifications for the component-specific

ARMA or ADL-models have been found, that the indirect forecasts dominate the

corresponding direct model. Indirect forecasts perform best when the information set is

widened, allowing different exogenous explanatory variables to enter in each component-

specific model. It should however be noted that in the pre-crisis period the best indirect

forecasts only marginally beat the best direct forecasts, and that this can partly be related to

the strong conditioning assumptions. Yet, even if a systematic superiority of the indirect

forecasting approach would be difficult to assert on the mere basis of the results of this paper,its use in practice nonetheless seems fully warranted and justifies further work on the

refinement of component-specific models.

An important lesson from the literature has been that the forecasting accuracy of models is

sensitive to the period in which they are estimated and evaluated, and that conclusions

regarding their merit may consequently be short-lived. The second objective of the paper has

been to illustrate this time-sensitivity and to gauge the impact of the crisis by repeating the

comparative assessment over two different sample periods. The rise in forecast errors of all

models, confirms that inflation forecasting has become substantially more difficult after the

onset of the crisis. However, the deterioration of the different models has been uneven: in

general, the performance of slightly more elaborated models – i.e. ARMA- and ADL-modelsselected on the basis of a penalty function – and in particular of indirect forecasts, has

improved during the crisis relative to simple econometric benchmarks or rules of thumb.

Indeed, while the model comparison during the pre-crisis period would have backed the

conclusions of earlier studies emphasising the virtues of simple models – including the central

bank’s inflation target – the comparative evaluation during the crisis would cast doubts on

those very same conclusions.

Future analysis on the specification of inflation forecasting models will need to take into

account the distortions caused by the commodity price swings and by the crisis after 2007. If

the choice of the forecasting model is made on the basis of past observations, e.g. by

performing an out-of-sample evaluation as in this paper, the question will arise how inflation



20

data from the crisis should be included in the model estimation, but also whether it seems

right to use the crisis as an evaluation period.



21

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Meyler, Aidan, Goeff Kenny and Terry Quinn, 1998, Forecasting Irish Inflation using

ARIMA models, Research Technical Paper 3/RT/98, Central Bank of Ireland, December 1998.

Moser, Gabriel, Fabio Rumler and Johann Scharler, 2004, Forecasting Austrian Inflation,

OeNB Working Paper 91, September 2004.

Stock, James and Mark Watson, 1999, Forecasting inflation, Journal of Monetary Economics

44 (1999) 293-335.

Svensson, Lars E. O., 1997, Inflation forecast targeting: Implementing and monitoringinflation targets, European Economic Review, Elsevier, vol. 41(6), pages 1111-1146, June.



22

Annex 1: Infla tion forec asts and presenta tion of data

Tab le A.1: Infla tion forec asts for 2008 and 2009 by ECB/Eurosystem, Europ ean

Co mmission a nd Survey o f Professiona l Forecasters

2008 2009

December 2006 1,9

March 2007 2,0

June 2007 2,0

September 2007 2,0

December 2007 2,5 1,8

March 2008 2,9 2,1

June 2008 3,4 2,4

September 2008 3,5 2,6

December 2008 3,3 1,4March 2009 0,4

June 2009 0,3

September 2009 0,4

December 2009 0,3

European Commission Spring and Autumn forecasts

2008 2009

Autumn (Nov 2006) 1,9

Spring (May 2007) 1,9

Autumn (Nov 2007) 2,1 2,0

Spring (April 2008) 3,2 2,2Autumn (Oct 2008) 3,5 2,2

Spring (May 2009) 0,4

Autumn (Nov 2009) 0,3

Survey of Professional Forecasters

2008 2009

November 2006 1,9

May 2007 1,9

October 2007 2,0 2,0

May 2008 3,1 2,1

October 2008 3,4 2,2

May 2009 0,5

October 2009 0,3

Average inflation 3,3 0,3

ECB and Eurosystem staff macroeconomic projections for the euro area

(*)

Note: (*) The figure refers to the mid-point of the published forecast. June and December forecasts are prepared

by ECB and Eurosystem staff. March and September forecasts are propared by ECB staff.

Source: ECB Monthly Bulletin, various editions.



23

Figure A.1. HICP indices, annual and monthly inflation; overall and by component

(1996:01-2010:12)

-2

-1

0

1

2

3

4

5

6

4.40

4.44

4.48

4.52

4.56

4.60

4.64

4.68

4.72

1996 1998 2000 2002 2004 2006 2008 2010

MC P00 Y CP00 C P00_LOG

cp00

p e r c e n t

l o g of i n d ex

-16

-12

-8

-4

0

4

8

12

16

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5.0

1996 1998 2000 2002 2004 2006 2008 2010

MEN RGY Y ENRGY EN RGY _LOG

enrgy

p e r c e n t

l o g of i n d ex

-2

0

2

4

6

8

10

12

4.40

4.45

4.50

4.55

4.60

4.65

4.70

4.75

1996 1998 2000 2002 2004 2006 2008 2010

MFOODUNPYFOODUNP

FOODUNP_LOG

foodunp

p e r c e n t

l o g of i n d ex

-1

0

1

2

3

4

5

6

7

8

4.35

4.40

4.45

4.50

4.55

4.60

4.65

4.70

4.75

4.80

1996 1998 2000 2002 2004 2006 2008 2010

MFOODPROCYFOODPROC

FOODPROC_LOG

foodproc

p e r c e n t

l o g of i n d ex

-2

-1

0

1

2

3

4

5

6

4.35

4.40

4.45

4.50

4.55

4.60

4.65

4.70

4.75

1996 1998 2000 2002 2004 2006 2008 2010

MSER V Y SERV SER V_LOG

serv

p e r c e n t

l o g of i n d ex

-4

-3

-2

-1

0

1

2

3

4.52

4.54

4.56

4.58

4.60

4.62

4.64

4.66

1996 1998 2000 2002 2004 2006 2008 2010

MIGOODSXE

YIGOODSXE

IGOODSXE_LOG

igoodsxe

p e r c e n t

l o g of i n d ex

Note: the graphs display the patterns of monthly inflation (“m” prefix), annual inflation (“y” prefix), on the left

y-axis, and the logarithm of the price index, on the right y-axis.



24

Figure A.2. Intra-year pattern of monthly inflation; overall and by component

(1996:01-2010:12)

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2


Means by Season

MCP00 by Season

-6

-4

-2

0

2

4

6


Means by Season

MENRGY by Season

-2

-1

0

1

2

3

4


Means by Season

MFOODUNP by Season

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2


Means by Season

MFOODPROC by Season

-0.8

-0.4

0.0

0.4

0.8

1.2


Means by Season

MSERV by Season

-4

-3

-2

-1

0

1

2

3


Means by Season

MIGOODSXE by Season



25

Tab le A.2.1: Desc rip tive sta tistic s – c risis eva luation period (2005:08-2010:12)


Mean 1.94 4.71 2.56 2.10 0.66 2.09

Median 1.92 7.22 2.02 2.53 0.72 2.12

Maximum 4.06 17.01 7.20 4.63 1.18 2.81

Minimum -0.65 -14.25 0.35 -1.60 -0.12 1.18

Range 4.70 31.26 6.85 6.23 1.30 1.62

Std Dev 1.07 7.81 1.97 1.67 0.30 0.45


Mean 0.17 0.34 0.21 0.18 0.10 0.16

Median 0.24 0.43 0.13 0.12 0.21 0.15

Maximum 1.11 3.53 1.18 1.47 2.48 0.89

Minimum -0.83 -4.90 -0.12 -1.23 -3.14 -0.75

Range 1.94 8.43 1.31 2.70 5.62 1.64Std Dev 0.38 1.75 0.25 0.58 1.23 0.43




Tab le A.2.2: Desc rip tive statistic s – p re-c risis eva lua tion period (2002:08-2007:12)


Mean 2.17 5.39 2.75 1.86 0.74 2.46

Median 2.15 6.03 2.67 1.66 0.79 2.51

Maximum 3.07 14.93 5.10 4.63 1.33 3.35

Minimum 1.61 -2.04 1.45 -1.52 -0.02 1.84Range 1.45 16.97 3.64 6.15 1.35 1.51

Std Dev 0.29 4.52 0.84 1.46 0.31 0.33


Mean 0.19 0.50 0.25 0.17 0.09 0.19

Median 0.25 0.45 0.15 0.23 0.16 0.15

Maximum 0.77 3.41 1.18 1.45 1.64 0.94

Minimum -0.60 -3.21 -0.11 -1.36 -2.06 -0.53

Range 1.37 6.62 1.30 2.81 3.70 1.47

Std Dev 0.29 1.45 0.28 0.61 0.94 0.38






26

Annex 2: Sta tionarity ana lysis

Tab le A.3 Aug mented Dickey-Fuller (ADF) test – Samp le: 1997:02-2012:02ADF-test cp00 enrgy foodproc foodunp igoodsxe serv

1% 5% 10%

log constant and 0 -3,09 -2,38 -2,16 -2,36 -7,99 -3,75 -4,01 -3,44 -3,14

trend 1 -3,4 -3,02 -2,34 -3,38 -14,17 -3,12

2 -3,17 -3,16 -2,65 -3,24 -10,85 -3

3 -2,85 -3,22 -2,79 -3,28 -9,82 -1,81

SIC -3,93 -3,02 -2,65 -3,86 -3,29 -3,81

AIC -3,33 -3,02 -3,03 -3,86 -2,54 -3,81

constant 0 -11,64 -9,71 -8,49 -9,78 -10,84 -15,46 -3,47 -2,88 -2,58

1 -9,55 -7,47 -5,48 -8,39 -14,15 -10,5

2 -8,85 -6,42 -4,66 -7,21 -13,2 -12,32

3 -8,58 -5,93 -4,23 -6,6 -26,81 -10,84

SIC -2,91 -9,71 -5,48 -2,55 -3,19 -0,85

AIC -3,21 -9,71 -2,89 -2,86 -3,19 -0,85

constant 0 -2,09 -2,08 -1,35 -2,11 -3,45 -1,83 -3,47 -2,88 -2,58

1 -2,65 -2,78 -2,19 -2,79 -3,72 -0,81

2 -3,06 -2,94 -2,91 -3,19 -2,97 -0,83

3 -2,92 -3,28 -2,92 -3,23 -2,7 -1,02

SIC -2,55 -2,77 -2,32 -2,79 -3,38 -2,67AIC -2,55 -2,77 -2,32 -2,67 -3,73 -2,21

d1d12 constant 0 -10,28 -9,84 -8,15 -9,94 -12,22 -20,67 -3,47 -2,88 -2,58

1 -7,1 -7,52 -5,24 -7,42 -11,23 -10,8

2 -6,64 -5,98 -4,89 -6,32 -9,36 -7,31

3 -5,24 -5,06 -3,78 -5,96 -9,2 -5,44

SIC -5,97 -6,16 -4,25 -9,94 -4,47 -20,67

AIC -5,97 -6,16 -4,25 -5,11 -4,47 -3,1

Critical values

Monthly

changes (d1)

Annual changes

(d12)

Deterministic

term

No. of lagged

differences

Philips-Peron (PP) test – Samp le: 1997:02-2012:02

PP-test cp00 enrgy foodproc foodunp igoodsxe serv

1% 5% 10%

log constant and -3,08 -2,86 -2,4 -2,89 -7,31 -3,68 -4,01 -3,44 -3,14

trend

Monthly constant -12,23 -9,7 -9,17 -9,81 -15,06 -20,43 -3,47 -2,88 -2,58

changes (d1)

Annual constant -2,75 -2,93 -2,44 -2,74 -3,68 -1,6 -3,47 -2,88 -2,58

changes (d12)

d1d12 constant -10,42 -9,99 -8,87 -9,94 -21,02 -19 -3,47 -2,88 -2,58

Deterministic

term

Critical values



27

Annex 3: Pre-selec tion o f exogenous va riab les

Tab le A.4: List of e xogeno us va riab les and abbrevia tions

oileur World, Energy, Oil, Crude Oil - North Sea (Brent), Dated, Close, EUR

oilusd World, Energy, Oil, Crude Oil - North Sea (Brent), Dated, Close, USDhwwieur Euro Zone, HWWI, Total Index, Average, EUR

hwwixeneur Euro Zone, HWWI, Total Index excluding Energy, Average, EUR

hwwiarm World, HWWI, Agricultural Raw Materials Index, Average, EUR

hwwicer World, HWWI, Cereals Index, Average, EUR

hwwicoal World, HWWI, Coal Index, Average, EUR

hwwicoil World, HWWI, Crude Oil Index, Average, EUR

hwwienrm World, HWWI, Energy Raw Materials Index, Average, EUR

hwwifood World, HWWI, Food Index, Average, EUR

hwwiind World, HWWI, Industrial Raw Materials Index, Average, EUR

hwwiiost World, HWWI, Iron Ore and Steel Scrap Index, Average, EUR

hwwinfm World, HWWI, Non-ferrous Metals Index, Average, EUR

hwwiseed World, HWWI, Oilseeds and Oils Index, Average, EUR

hwwitex World, HWWI, Textile Fibres Index, Average, EURhwwiexen World, HWWI, Total Index excluding Energy, Average, EUR

hwwi World, HWWI, Total Index, Average, EUR

eurusd Euro Zone, Spot Rates, EUR/USD, Close, USD

eer21 Euro Zone, ECB, EER-21 Nominal Effective Exchange Rate Index, Euro 16, EUR

eer41 Euro Zone, ECB, EER-41 Nominal Effective Exchange Rate Index, Euro 16, EUR

reer21 Euro Zone, ECB, EER-21 Real CPI Effective Exchange Rate Index, Euro 16, EUR

reer41 Euro Zone, ECB, EER-41 Real CPI Effective Exchange Rate Index, Euro 16, EUR

iptotencon Eurostat, Euro Zone, Production, Overall, NACE Rev.2 B_C_X_MIG_NRG, Total, excluding construction

and energy, Cal Adj, Index, EUR, 2005=100

iptotcon Eurostat, Euro Zone, Production, Overall, NACE Rev.2 B-D, Total, excluding construction, Cal Adj, Index,

EUR, 2005=100iptoten Eurostat, Euro Zone, Production, Overall, NACE Rev.2 B-D_F, Industry including construction, Cal Adj,

Index, EUR, 2005=100

ipcapg Eurostat, Euro Zone, Production, Aggregates, NACE Rev.2 MIG_CAG, Capital goods, Cal Adj, Index, EUR,

2005=100

ipconsg Eurostat, Euro Zone, Production, Aggregates, NACE Rev.2 MIG_COG, Consumer goods, Cal Adj, Index,

EUR, 2005=100

ipintgds Eurostat, Euro Zone, Production, Aggregates, NACE Rev.2 MIG_ING, Intermediate goods, Cal Adj, Index,

EUR, 2005=100

ipener Eurostat, Euro Zone, Production, Aggregates, NACE Rev.2 MIG_NRG_X_E, Energy, Cal Adj, Index, EUR,

2005=100

iocapg Eurostat, Euro Zone, New Orders, Aggregates, NACE Rev.2 MIG_CAG_ORD, Capital goods, Index, EUR,

2005=100ioconsd Eurostat, Euro Zone, New Orders, Aggregates, NACE Rev.2 MIG_DCOG_ORD, Consumer durables, Index,

EUR, 2005=100

iointg Eurostat, Euro Zone, New Orders, Aggregates, NACE Rev.2 MIG_ING_ORD, Intermediate goods, Index,

EUR, 2005=100

hhfinsit12 DG ECFIN, Euro Zone, Consumer Surveys, Financial situation of households over next 12 months, SA

hhecosit12 DG ECFIN, Euro Zone, Consumer Surveys, General economic situation over next 12 months, SA

majpur12 DG ECFIN, Euro Zone, Consumer Surveys, Major purchases over next 12 months, SA

pritre12 DG ECFIN, Euro Zone, Consumer Surveys, Price trends over next 12 months, SA

sav12 DG ECFIN, Euro Zone, Consumer Surveys, Savings over next 12 months, SA

uetot_lm Eurostat, Euro Zone, Unemployment, Overall, Total

uer_lm Eurostat, Euro Zone, Unemployment, Rate, Total

Commodity prices

Exchange rate

Industrial production

Industrial orders

Surveys

Labour market

Source: Ecowin



28

Tab le A.5: Lead ing ind ica to r ana lysis for head line infla tion (1997:02-2010:12)cp00 F-stat p-value R-bar2 F-stat p-value R-bar2 F-stat p-value R-bar2 F-stat p-value R-bar2

dln_oileur 8.66 0.00 0.63 5.61 0.00 0.56 3.49 0.00 0.50 1.43 0.15 0.41

dln_oilusd 8.02 0.00 0.64 5.67 0.00 0.58 3.40 0.00 0.51 1.56 0.11 0.43

dln_hwwieur 9.60 0.00 0.67 5.71 0.00 0.58 2.95 0.00 0.49 1.14 0.34 0.41

dln_hwwixeneur 3.79 0.00 0.52 3.42 0.00 0.51 1.50 0.13 0.43 0.66 0.80 0.38dln_hwwiarm 1.86 0.04 0.45 2.17 0.01 0.46 1.37 0.18 0.42 1.02 0.44 0.40

dln_hwwicer 3.39 0.00 0.51 3.31 0.00 0.51 1.55 0.11 0.43 1.02 0.44 0.40

dln_hwwicoal 4.02 0.00 0.53 3.90 0.00 0.53 1.48 0.13 0.43 1.88 0.04 0.45

dln_hwwicoil 7.78 0.00 0.63 5.25 0.00 0.57 3.16 0.00 0.50 1.06 0.40 0.40

dln_hwwienrm 8.22 0.00 0.64 5.55 0.00 0.58 3.21 0.00 0.50 1.14 0.34 0.41

dln_hwwifood 2.80 0.00 0.49 2.82 0.00 0.49 1.41 0.16 0.42 0.93 0.52 0.40

dln_hwwiind 3.13 0.00 0.50 2.54 0.00 0.47 1.38 0.18 0.42 0.88 0.58 0.39

dln_hwwiiost 3.38 0.00 0.51 3.28 0.00 0.50 3.32 0.00 0.51 1.38 0.18 0.42

dln_hwwinfm 3.01 0.00 0.49 1.95 0.03 0.45 1.10 0.36 0.41 0.66 0.79 0.38

dln_hwwiseed 1.80 0.05 0.44 1.95 0.03 0.45 1.22 0.27 0.41 1.27 0.24 0.42

dln_hwwitex 1.81 0.05 0.44 1.84 0.04 0.44 1.24 0.26 0.41 0.54 0.89 0.37

dln_hwwiexen 3.31 0.00 0.51 2.95 0.00 0.49 1.24 0.26 0.41 0.66 0.80 0.38

dln_hwwi 9.02 0.00 0.65 5.70 0.00 0.58 3.01 0.00 0.50 1.08 0.38 0.41

dln_eurusd 1.35 0.19 0.42 1.64 0.08 0.43 0.79 0.67 0.39 0.91 0.54 0.40

dln_eer21 1.13 0.34 0.41 1.43 0.16 0.42 0.61 0.84 0.38 1.01 0.45 0.40

dln_eer41 1.11 0.36 0.41 1.40 0.17 0.42 0.63 0.82 0.38 0.91 0.54 0.40dln_reer21 1.20 0.28 0.41 1.42 0.16 0.42 0.58 0.87 0.38 0.93 0.52 0.40

dln_reer41 1.15 0.33 0.41 1.37 0.18 0.42 0.58 0.86 0.38 0.88 0.58 0.39

dln_iptotencon 5.57 0.00 0.58 5.62 0.00 0.58 4.43 0.00 0.55 4.41 0.00 0.55

dln_iptotcon 6.00 0.00 0.59 6.29 0.00 0.60 5.15 0.00 0.57 5.11 0.00 0.58

dln_iptoten 6.23 0.00 0.60 6.35 0.00 0.60 5.24 0.00 0.57 5.41 0.00 0.58

dln_ipcapg 6.44 0.00 0.60 6.34 0.00 0.60 5.41 0.00 0.58 4.91 0.00 0.57

dln_ipconsg 4.38 0.00 0.54 4.42 0.00 0.54 4.94 0.00 0.56 5.02 0.00 0.57

dln_ipintgds 5.87 0.00 0.59 5.56 0.00 0.58 4.41 0.00 0.55 4.61 0.00 0.56

dln_ipener 4.32 0.00 0.54 4.77 0.00 0.56 4.60 0.00 0.55 5.23 0.00 0.58

dln_iocapg 5.26 0.00 0.57 5.21 0.00 0.57 2.80 0.00 0.49 3.10 0.00 0.50

dln_ioconsd 4.73 0.00 0.55 4.42 0.00 0.54 3.04 0.00 0.50 2.97 0.00 0.50

dln_iointg 4.72 0.00 0.55 4.99 0.00 0.56 2.39 0.01 0.47 2.28 0.01 0.47

plv_hhfinsit12 0.62 0.83 0.38 0.63 0.82 0.38 1.01 0.45 0.40 0.82 0.64 0.39plv_hhecosit12 0.82 0.63 0.39 0.83 0.63 0.39 1.38 0.18 0.42 1.08 0.39 0.41

plv_majpur12 1.62 0.09 0.43 1.66 0.08 0.43 1.07 0.39 0.40 1.11 0.35 0.41

plv_pritre12 1.79 0.05 0.44 1.73 0.06 0.44 1.68 0.07 0.44 0.75 0.72 0.39

dlv_sav12 1.32 0.21 0.42 1.31 0.22 0.42 1.36 0.19 0.42 1.56 0.11 0.43

dln_uetot_lm 3.40 0.00 0.51 2.54 0.00 0.47 2.98 0.00 0.50 4.28 0.00 0.55

dln_uer_lm 4.35 0.00 0.54 2.75 0.00 0.48 3.02 0.00 0.50 4.08 0.00 0.54

Industrial production

Industrial orders

Surveys

Labour market

k=0 k=1 k=6 k=12

Commodity prices

Exchange rate

Note: the adjusted coefficient of determination of the (restricted) AR(12) model is 0.39. "dln" is the first

difference of the logarithmic series; "dlv" is the first difference of the original series; "plv" is the percentage

change of the original series.



29

Annex 4: Rec ursive Root Mea n Squared Forec ast Error

The forecast accuracy of a model m can be measured by the standard recursive Root Mean

Squared Forecast Error (RMSFE) in a simulated out-of-sample forecast exercise. The RMSFE

is obtained by first splitting the sample (of length N ) into two parts: the model is fitted to the

first subsample (of length N-n), running up to month t , and the series is then forecasted "out-of-sample". The forecast errors – the difference between the expectation of annual inflation at

time t+h conditional on the information at time t ,21

and the actual value of annual inflation –

are then computed over the second (shorter) sub-sample (of length n) and stored.22

The

maximum number of comparable forecasts thus corresponds to the number of remaining

observations in the second sub-sample. For a given forecast horizon, the RMSFE is given by

the following expression:

( )2 / 1

2

/ ˆ)( ÷øö

çè

æ -= å ++ T h RMSFE T

t ht t

mmht p p ,

Where mht +

p ̂ is the annual inflation forecast generated by candidate model m, at an h-month

horizon, conditional on the information or assumptions at time t . π t+h is the actual inflation

rate at time t+h, while T represents the number of observations over which the model is

evaluated.

The first sub-sample is recursively extended by one observation, and the estimation and

comparison procedure above is repeated. While the first sub-sample thus gradually

approaches the size of the full sample, the maximum comparable forecast horizon is reduced

by one period at each step and thus approaches zero. More generally, for an h-step-ahead

forecast, there will be n-h+1 possible forecast observations.23

If a model is to be evaluated upto h steps ahead, the last recursive estimation should yield h comparable forecasts, implying

that the last h available observations will not be used for the recursive estimation but only for

evaluation purposes. This also implies that the same number of observations, T (=n- hmax+1),

is used to compute the RMSFE at each forecast horizon. In this paper, the evaluation period

(T ) is set to 48 months (i.e. 4 years), and the maximum forecast horizon (hmax) is set to 18

months.

21 If the model contains exogenous variables, the forecast needs to be conditioned on a specific path assumed for

the latter beyond time t.22

Models are compared on how accurately they predict annual inflation, which is the natural yardstick for

inflation. This implies that forecasts obtained from models that are based on other transformations of the original

price level series first need to be transformed into annual price changes.23 Starting with a given sub-sample, one will obtain n possible one-step-ahead forecasts, n-1 two-step ahead

forecasts etc. and one n-step-ahead forecast.



Annex 5: Results

Tab le.A.6: RMSFEs fo r eva lua tion sam ple inc lud ing c risis

Horizon: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 to 6 7 to 12 13 to 18 1 to 18

Benchmarks

ECB 1,03 1,08 1,12 1,15 1,17 1,18 1,18 1,19 1,19 1,19 1,19 1,19 1,19 1,19 1,19 1,18 1,18 1,19 1,12 1,19 1,19 1,17

Naive 0,31 0,51 0,70 0,87 1,04 1,18 1,31 1,44 1,57 1,68 1,77 1,84 1,89 1,90 1,90 1,89 1,86 1,84 0,77 1,60 1,88 1,42

AR(1) 0,37 0,57 0,72 0,81 0,87 0,90 1,02 1,12 1,19 1,22 1,23 1,24 1,24 1,24 1,24 1,24 1,23 1,23 0,71 1,17 1,24 1,04

ARMA(1,1) 0,37 0,56 0,70 0,79 0,85 0,89 1,01 1,10 1,17 1,19 1,20 1,22 1,22 1,22 1,22 1,21 1,21 1,20 0,69 1,15 1,21 1,02

AR(12) 0,31 0,53 0,74 0,91 1,06 1,17 1,29 1,40 1,49 1,57 1,64 1,69 1,70 1,71 1,69 1,68 1,64 1,61 0,79 1,51 1,67 1,32

Seas. Dummies 0,26 0,41 0,54 0,64 0,73 0,81 0,91 1,00 1,08 1,14 1,19 1,24 1,24 1,24 1,24 1,23 1,23 1,23 0,57 1,09 1,23 0,96

Univariate (AIC) AR MA

U.1 10 6 0,31 0,48 0,66 0,81 0,94 1,01 1,11 1,20 1,26 1,33 1,36 1,39 1,38 1,38 1,35 1,33 1,31 1,29 0,70 1,27 1,34 1,11

U.2 8 9 0,27 0,44 0,60 0,71 0,83 0,92 1,05 1,19 1,30 1,40 1,48 1,56 1,57 1,56 1,55 1,52 1,47 1,40 0,63 1,33 1,51 1,16

U.3 10 9 0,30 0,50 0,70 0,85 1,00 1,12 1,23 1,34 1,43 1,50 1,54 1,57 1,56 1,55 1,53 1,52 1,49 1,46 0,75 1,43 1,52 1,23

U.4 5 6 0,26 0,42 0,57 0,66 0,74 0,82 0,91 1,00 1,09 1,16 1,21 1,26 1,27 1,27 1,27 1,27 1,25 1,24 0,58 1,11 1,26 0,98

Univariate (SIC) AR MA

U.1 10 6 0,31 0,48 0,66 0,81 0,94 1,01 1,11 1,20 1,26 1,33 1,36 1,39 1,38 1,38 1,35 1,33 1,31 1,29 0,70 1,27 1,34 1,11U.2 7 5 0,24 0,42 0,56 0,67 0,78 0,86 0,97 1,08 1,16 1,24 1,31 1,37 1,38 1,38 1,38 1,37 1,35 1,32 0,59 1,19 1,36 1,05

U.3 0 0 0,29 0,48 0,66 0,80 0,95 1,07 1,19 1,31 1,43 1,53 1,62 1,69 1,72 1,73 1,73 1,72 1,69 1,66 0,71 1,46 1,71 1,29

U.4 5 6 0,26 0,42 0,57 0,66 0,74 0,82 0,91 1,00 1,09 1,16 1,21 1,26 1,27 1,27 1,27 1,27 1,25 1,24 0,58 1,11 1,26 0,98

ADL Specification Y-lags X-lags

oileur B.3 7 6 0,19 0,28 0,36 0,41 0,48 0,52 0,61 0,70 0,79 0,87 0,93 1,00 1,02 1,04 1,05 1,06 1,04 1,05 0,37 0,82 1,04 0,74

oilusd B.3 7 9 0,19 0,27 0,34 0,38 0,44 0,48 0,56 0,64 0,72 0,80 0,86 0,92 0,93 0,95 0,95 0,96 0,94 0,94 0,35 0,75 0,95 0,68

hwwieur B.3 7 6 0,19 0,27 0,35 0,38 0,43 0,45 0,53 0,62 0,70 0,77 0,82 0,88 0,90 0,92 0,93 0,93 0,93 0,94 0,34 0,72 0,92 0,66

hwwixeneur B .1 6 2 0,31 0,44 0,56 0,63 0,68 0,71 0,79 0,87 0,94 0,99 1,03 1,08 1,09 1,12 1,13 1,13 1,14 1,14 0,55 0,95 1,12 0,88

hwwiarm B.3 6 0 0,25 0,42 0,56 0,67 0,77 0,84 0,94 1,04 1,14 1,21 1,27 1,32 1,32 1,32 1,31 1,29 1,27 1,25 0,59 1,16 1,29 1,01

hwwicer B.1 8 9 0,32 0,44 0,57 0,64 0,69 0,70 0,75 0,81 0,84 0,86 0,86 0,87 0,87 0,87 0,89 0,90 0,90 0,89 0,56 0,83 0,89 0,76

hwwicoal B.1 6 19 0,33 0,44 0,53 0,60 0,65 0,66 0,75 0,84 0,90 0,94 0,96 0,98 0,97 0,96 0,95 0,95 0,95 0,94 0,54 0,90 0,95 0,79

hwwicoil B.3 7 6 0,19 0,28 0,36 0,41 0,47 0,52 0,60 0,69 0,78 0,86 0,92 0,99 1,01 1,03 1,04 1,05 1,03 1,04 0,37 0,80 1,03 0,74

hwwienrm B.3 7 9 0,19 0,28 0,36 0,40 0,47 0,51 0,58 0,67 0,76 0,85 0,91 0,98 1,00 1,02 1,02 1,03 1,02 1,02 0,37 0,79 1,02 0,73

hwwifood B.1 8 9 0,31 0,46 0,61 0,69 0,75 0,77 0,84 0,92 0,96 0,98 0,99 1,00 1,00 1,00 1,00 1,01 1,01 1,00 0,60 0,95 1,00 0,85

hwwiind B.3 6 0 0,24 0,39 0,52 0,61 0,71 0,78 0,88 0,98 1,08 1,16 1,22 1,28 1,29 1,29 1,29 1,28 1,27 1,25 0,54 1,10 1,28 0,97

hwwiiost B.1 7 16 0,32 0,48 0,57 0,63 0,66 0,68 0,76 0,83 0,87 0,89 0,92 0,96 0,99 1,02 1,03 1,05 1,06 1,06 0,55 0,87 1,03 0,82

hwwinfm B.3 6 0 0,24 0,38 0,51 0,60 0,70 0,77 0,88 0,98 1,08 1,16 1,23 1,29 1,30 1,30 1,29 1,29 1,27 1,26 0,53 1,10 1,29 0,97

hwwiseed B.4 6 9 0,26 0,42 0,55 0,63 0,71 0,76 0,83 0,92 1,01 1,07 1,11 1,15 1,14 1,14 1,13 1,12 1,10 1,09 0,55 1,01 1,12 0,90

hwwiexen B.3 6 2 0,24 0,38 0,51 0,59 0,68 0,73 0,83 0,92 1,01 1,09 1,14 1,20 1,21 1,22 1,22 1,21 1,21 1,20 0,52 1,03 1,21 0,92

hwwi B.3 7 6 0,19 0,28 0,35 0,38 0,44 0,47 0,55 0,63 0,72 0,79 0,85 0,91 0,93 0,96 0,96 0,97 0,97 0,97 0,35 0,74 0,96 0,68

eurusd B.3 6 n.a. 0,25 0,41 0,56 0,66 0,76 0,83 0,93 1,03 1,12 1,19 1,25 1,30 1,29 1,29 1,28 1,27 1,25 1,24 0,58 1,14 1,27 0,99

iptotencon B.1 11 9 0,27 0,44 0,60 0,71 0,81 0,85 0,90 0,92 0,94 0,95 0,97 0,99 0,97 0,98 0,97 0,95 0,91 0,88 0,61 0,94 0,94 0,83

iptotcon B.2 6 8 0,25 0,42 0,58 0,70 0,81 0,87 0,94 0,98 1,03 1,06 1,08 1,09 1,06 1,05 1,01 0,97 0,92 0,89 0,61 1,03 0,98 0,87

iptoten B.3 6 1 0,24 0,40 0,54 0,65 0,75 0,82 0,91 1,00 1,09 1,16 1,21 1,25 1,24 1,24 1,22 1,20 1,16 1,14 0,57 1,10 1,20 0,96

ipcapg B.2 8 8 0,25 0,42 0,57 0,68 0,78 0,83 0,89 0,92 0,95 0,98 0,99 1,00 0,99 0,99 0,97 0,95 0,92 0,90 0,59 0,96 0,95 0,83

ipconsg B.3 6 6 0,25 0,41 0,56 0,65 0,77 0,84 0,95 1,05 1,14 1,22 1,29 1,34 1,34 1,34 1,33 1,31 1,27 1,25 0,58 1,17 1,31 1,02

ipintgds B.2 11 10 0,26 0,43 0,58 0,68 0,76 0,80 0,87 0,95 1,05 1,14 1,23 1,31 1,33 1,35 1,34 1,32 1,26 1,22 0,59 1,09 1,30 0,99

ipener B.3 6 13 0,26 0,44 0,59 0,68 0,78 0,82 0,88 0,95 1,04 1,11 1,16 1,19 1,18 1,17 1,15 1,13 1,11 1,09 0,59 1,05 1,14 0,93

iocapg B.2 0 7 0,25 0,38 0,50 0,58 0,67 0,71 0,76 0,81 0,87 0,91 0,94 0,98 0,98 0,97 0,94 0,92 0,88 0,86 0,52 0,88 0,93 0,77

ioconsd B.1 8 12 0,28 0,48 0,66 0,83 0,96 1,04 1,14 1,20 1,24 1,27 1,31 1,34 1,34 1,34 1,33 1,33 1,32 1,31 0,71 1,25 1,33 1,10

iointg B.1 6 19 0,28 0,42 0,56 0,64 0,68 0,70 0,74 0,76 0,80 0,84 0,87 0,89 0,89 0,90 0,92 0,94 0,95 0,97 0,55 0,81 0,93 0,76

hhfinsit12 B.3 6 3 0,25 0,41 0,56 0,66 0,76 0,83 0,93 1,03 1,13 1,21 1,27 1,32 1,32 1,32 1,31 1,30 1,27 1,26 0,58 1,15 1,30 1,01

hhecosit12 B.3 6 n.a. 0,25 0,41 0,56 0,66 0,76 0,83 0,93 1,03 1,12 1,19 1,25 1,30 1,29 1,29 1,28 1,27 1,25 1,24 0,58 1,14 1,27 0,99

majpur12 B.1 8 3 0,34 0,52 0,69 0,82 0,92 0,97 1,07 1,15 1,20 1,23 1,24 1,25 1,23 1,22 1,22 1,22 1,22 1,20 0,71 1,19 1,22 1,04pritre12 B.3 6 0 0,25 0,41 0,55 0,64 0,74 0,80 0,90 0,99 1,09 1,16 1,23 1,29 1,32 1,34 1,36 1,37 1,37 1,37 0,56 1,11 1,35 1,01

sav12 B.3 6 1 0,24 0,40 0,54 0,63 0,71 0,77 0,85 0,94 1,02 1,09 1,13 1,17 1,16 1,16 1,14 1,13 1,11 1,10 0,55 1,03 1,13 0,91

uetot_lm B.3 6 0 0,24 0,38 0,50 0,58 0,67 0,72 0,80 0,87 0,95 1,01 1,06 1,09 1,08 1,08 1,08 1,08 1,06 1,05 0,51 0,96 1,07 0,85

uer_lm B.3 6 0 0,23 0,37 0,50 0,58 0,66 0,72 0,80 0,87 0,95 1,01 1,06 1,09 1,08 1,09 1,09 1,09 1,07 1,06 0,51 0,96 1,08 0,85

Agg-AR(1) 0,36 0,57 0,73 0,83 0,88 0,89 1,00 1,11 1,19 1,24 1,24 1,24 1,24 1,24 1,24 1,24 1,23 1,23 0,71 1,17 1,24 1,04

Agg-ARMA(1,1) 0,36 0,58 0,73 0,81 0,86 0,85 0,96 1,08 1,18 1,23 1,25 1,24 1,24 1,25 1,25 1,25 1,24 1,23 0,70 1,16 1,24 1,03

Agg-AR(12) 0,23 0,38 0,54 0,68 0,82 0,93 1,04 1,14 1,23 1,31 1,39 1,47 1,49 1,50 1,50 1,49 1,47 1,45 0,60 1,26 1,48 1,12

Agg-Seas. Dummies 0,27 0,43 0,56 0,64 0,73 0,80 0,90 1,00 1,09 1,15 1,19 1,24 1,24 1,24 1,24 1,23 1,23 1,23 0,57 1,09 1,23 0,97

Agg-ARMA (identical) 0,21 0,36 0,52 0,62 0,72 0,82 0,92 1,00 1,07 1,15 1,21 1,28 1,31 1,32 1,32 1,32 1,31 1,30 0,54 1,11 1,31 0,99

Agg-ARMA (component-specific) 0,20 0,32 0,45 0,54 0,65 0,74 0,82 0,92 0,99 1,07 1,13 1,19 1,20 1,21 1,21 1,20 1,20 1,20 0,48 1,02 1,20 0,90

Agg-oilusd (identical) 0,16 0,23 0,31 0,36 0,44 0,49 0,56 0,62 0,67 0,73 0,79 0,84 0,86 0,88 0,89 0,90 0,91 0,91 0,33 0,70 0,89 0,64

Agg-oilusd (component-specific) 0,16 0,21 0,29 0,34 0,42 0,47 0,53 0,60 0,65 0,70 0,75 0,80 0,82 0,85 0,86 0,87 0,89 0,89 0,32 0,67 0,86 0,62

Agg-multivariate (component-specific) 0,16 0,21 0,28 0,31 0,36 0,38 0,39 0,42 0,45 0,48 0,50 0,53 0,53 0,53 0,53 0,53 0,53 0,54 0,28 0,46 0,53 0,42

Direct forecasts

Indirect forecasts



31

Tab le.A.7: RMSFEs for p re-c risis eva lua tion sam ple

Horizon: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 to 6 7 to 12 13 to 18 1 to 18

Benchmarks

ECB 0,34 0,34 0,34 0,34 0,33 0,33 0,33 0,32 0,31 0,31 0,31 0,31 0,31 0,31 0,31 0,33 0,36 0,40 0,34 0,32 0,34 0,33

Naive 0,18 0,24 0,30 0,33 0,34 0,34 0,34 0,35 0,34 0,35 0,37 0,40 0,39 0,38 0,36 0,35 0,35 0,36 0,29 0,36 0,36 0,34

AR(1) 0,29 0,41 0,49 0,51 0,49 0,46 0,52 0,58 0,58 0,55 0,48 0,38 0,37 0,37 0,37 0,38 0,41 0,44 0,44 0,52 0,39 0,45

ARMA(1,1) 0,29 0,40 0,47 0,49 0,47 0,44 0,49 0,55 0,55 0,52 0,45 0,36 0,36 0,36 0,35 0,36 0,40 0,43 0,42 0,49 0,38 0,43

AR(12) 0,20 0,27 0,32 0,35 0,35 0,35 0,35 0,36 0,36 0,35 0,34 0,33 0,33 0,34 0,34 0,35 0,37 0,39 0,31 0,35 0,35 0,34

Seas. Dummies 0,18 0,27 0,33 0,34 0,34 0,33 0,36 0,40 0,41 0,41 0,40 0,41 0,41 0,40 0,40 0,41 0,44 0,47 0,30 0,40 0,42 0,37

Univariate (AIC) AR MA

U.1 10 10 0,23 0,29 0,35 0,37 0,38 0,38 0,41 0,41 0,41 0,42 0,39 0,37 0,35 0,36 0,37 0,37 0,40 0,43 0,34 0,40 0,38 0,37

U.2 7 8 0,18 0,25 0,32 0,35 0,35 0,36 0,37 0,38 0,41 0,43 0,43 0,43 0,42 0,41 0,42 0,42 0,44 0,45 0,30 0,41 0,43 0,38

U.3 10 11 0,20 0,26 0,33 0,37 0,39 0,38 0,41 0,44 0,42 0,42 0,42 0,42 0,43 0,46 0,45 0,44 0,44 0,47 0,32 0,42 0,45 0,40

U.4 2 11 0,18 0,27 0,35 0,39 0,41 0,42 0,45 0,50 0,53 0,53 0,53 0,51 0,49 0,48 0,48 0,45 0,43 0,42 0,34 0,51 0,46 0,44

Univariate (SIC) AR MA

U.1 9 7 0,25 0,32 0,39 0,41 0,43 0,42 0,42 0,44 0,42 0,43 0,41 0,38 0,37 0,38 0,37 0,36 0,39 0,41 0,37 0,42 0,38 0,39

U.2 2 2 0,18 0,26 0,32 0,34 0,33 0,33 0,36 0,39 0,39 0,39 0,39 0,39 0,40 0,40 0,40 0,39 0,41 0,44 0,29 0,39 0,40 0,36

U.3 0 0 0,19 0,26 0,32 0,35 0,35 0,34 0,36 0,39 0,38 0,38 0,37 0,36 0,36 0,36 0,36 0,36 0,36 0,37 0,30 0,37 0,36 0,35

U.4 2 2 0,18 0,25 0,31 0,32 0,31 0,30 0,31 0,35 0,36 0,37 0,34 0,34 0,32 0,34 0,34 0,37 0,40 0,42 0,28 0,35 0,37 0,33

ADL Specification Y-lags X-lags

oileur B.4 7 1 0,16 0,19 0,24 0,26 0,26 0,25 0,26 0,28 0,28 0,29 0,29 0,29 0,28 0,27 0,27 0,27 0,29 0,31 0,23 0,28 0,28 0,26 oilusd B.4 7 1 0,15 0,19 0,23 0,24 0,24 0,24 0,24 0,26 0,26 0,27 0,27 0,25 0,24 0,23 0,22 0,22 0,24 0,26 0,22 0,26 0,23 0,24

hwwieur B.3 6 1 0,17 0,21 0,26 0,28 0,27 0,27 0,28 0,31 0,31 0,31 0,31 0,30 0,29 0,29 0,27 0,27 0,28 0,30 0,24 0,30 0,28 0,28

hwwixeneur B.2 4 1 0,19 0,24 0,29 0,32 0,34 0,33 0,34 0,35 0,33 0,32 0,32 0,32 0,32 0,32 0,32 0,32 0,34 0,37 0,29 0,33 0,33 0,32

hwwiarm B.2 6 1 0,19 0,23 0,28 0,30 0,32 0,31 0,32 0,34 0,33 0,32 0,33 0,35 0,35 0,35 0,35 0,35 0,37 0,39 0,27 0,33 0,36 0,32

hwwicer B.4 6 6 0,18 0,23 0,28 0,30 0,32 0,33 0,37 0,41 0,44 0,47 0,50 0,53 0,54 0,54 0,54 0,53 0,54 0,55 0,28 0,45 0,54 0,42

hwwicoal B.2 4 4 0,21 0,25 0,29 0,31 0,32 0,31 0,34 0,37 0,37 0,38 0,39 0,39 0,39 0,40 0,39 0,39 0,40 0,41 0,28 0,37 0,40 0,35

hwwicoil B .4 7 1 0,16 0,20 0,24 0,26 0,26 0,26 0,26 0,28 0,29 0,30 0,30 0,30 0,29 0,29 0,29 0,29 0,31 0,33 0,23 0,29 0,30 0,27

hwwienrm B.4 7 1 0,16 0,20 0,24 0,26 0,25 0,25 0,25 0,28 0,28 0,29 0,29 0,29 0,28 0,29 0,28 0,28 0,30 0,32 0,23 0,28 0,29 0,27

hwwifood B.4 11 6 0,18 0,20 0,24 0,24 0,24 0,24 0,27 0,31 0,33 0,34 0,35 0,35 0,35 0,36 0,36 0,36 0,36 0,38 0,22 0,32 0,36 0,30

hwwiind B.4 2 8 0,17 0,23 0,28 0,30 0,31 0,31 0,32 0,34 0,33 0,33 0,33 0,35 0,35 0,34 0,34 0,34 0,36 0,39 0,27 0,33 0,35 0,32

hwwiiost B .2 4 1 0,19 0,26 0,31 0,33 0,34 0,34 0,34 0,33 0,30 0,29 0,28 0,29 0,29 0,29 0,28 0,29 0,32 0,35 0,29 0,31 0,30 0,30

hwwinfm B.4 6 0 0,17 0,23 0,27 0,30 0,30 0,30 0,31 0,32 0,31 0,31 0,31 0,31 0,31 0,29 0,28 0,30 0,35 0,40 0,26 0,31 0,32 0,30

hwwiseed B.4 11 6 0,18 0,21 0,25 0,25 0,25 0,24 0,27 0,31 0,34 0,35 0,35 0,37 0,36 0,37 0,37 0,38 0,39 0,40 0,23 0,33 0,38 0,31

hwwitex B.2 4 n.a. 0,20 0,25 0,30 0,32 0,33 0,33 0,34 0,35 0,34 0,34 0,34 0,34 0,35 0,35 0,35 0,36 0,38 0,41 0,29 0,34 0,36 0,33

hwwiexen B.2 4 1 0,19 0,24 0,29 0,32 0,33 0,33 0,33 0,34 0,33 0,31 0,31 0,31 0,32 0,32 0,32 0,33 0,35 0,38 0,28 0,32 0,34 0,31

hwwi B.3 6 1 0,17 0,21 0,26 0,27 0,27 0,27 0,27 0,30 0,31 0,31 0,30 0,29 0,28 0,28 0,28 0,27 0,28 0,31 0,24 0,30 0,28 0,27

eurusd B.4 6 n.a. 0,17 0,22 0,27 0,30 0,31 0,31 0,33 0,35 0,36 0,36 0,38 0,39 0,39 0,39 0,39 0,40 0,43 0,46 0,26 0,36 0,41 0,35

eer21 B.4 6 n.a. 0,17 0,22 0,27 0,30 0,31 0,31 0,33 0,35 0,36 0,36 0,38 0,39 0,39 0,39 0,39 0,40 0,43 0,46 0,26 0,36 0,41 0,35

eer41 B.2 4 1 0,19 0,24 0,29 0,32 0,33 0,33 0,34 0,35 0,33 0,32 0,33 0,33 0,33 0,33 0,33 0,34 0,36 0,40 0,28 0,33 0,35 0,32

reer21 B.4 6 n.a. 0,17 0,22 0,27 0,30 0,31 0,31 0,33 0,35 0,36 0,36 0,38 0,39 0,39 0,39 0,39 0,40 0,43 0,46 0,26 0,36 0,41 0,35

reer41 B.2 4 1 0,20 0,25 0,30 0,32 0,34 0,33 0,35 0,36 0,34 0,34 0,34 0,35 0,35 0,35 0,35 0,36 0,39 0,42 0,29 0,35 0,37 0,33

iptotencon B.2 11 11 0,17 0,24 0,28 0,30 0,30 0,29 0,30 0,32 0,34 0,35 0,35 0,36 0,36 0,36 0,35 0,35 0,38 0,41 0,27 0,34 0,37 0,32

iptotcon B.2 6 13 0,16 0,22 0,26 0,28 0,29 0,29 0,30 0,31 0,32 0,32 0,34 0,36 0,35 0,35 0,36 0,37 0,41 0,45 0,25 0,33 0,38 0,32

iptoten B.2 6 16 0,18 0,25 0,32 0,36 0,37 0,37 0,36 0,36 0,33 0,33 0,35 0,39 0,39 0,39 0,38 0,38 0,41 0,45 0,31 0,35 0,40 0,35

ipcapg B.2 6 11 0,17 0,22 0,27 0,29 0,30 0,30 0,31 0,32 0,32 0,33 0,35 0,36 0,36 0,35 0,36 0,38 0,42 0,46 0,26 0,33 0,39 0,33

ipconsg B.2 4 4 0,17 0,23 0,28 0,31 0,32 0,32 0,34 0,35 0,35 0,35 0,36 0,37 0,37 0,37 0,37 0,39 0,42 0,45 0,27 0,35 0,39 0,34

ipintgds B.2 11 17 0,18 0,25 0,29 0,31 0,31 0,30 0,31 0,34 0,36 0,38 0,39 0,40 0,39 0,39 0,38 0,38 0,39 0,43 0,27 0,36 0,39 0,34

ipener B.2 10 15 0,19 0,25 0,29 0,31 0,31 0,30 0,31 0,34 0,35 0,35 0,35 0,33 0,30 0,30 0,29 0,30 0,33 0,36 0,27 0,34 0,31 0,31

iocapg B.2 10 11 0,19 0,25 0,30 0,31 0,31 0,29 0,30 0,33 0,35 0,37 0,37 0,38 0,37 0,37 0,37 0,36 0,36 0,38 0,28 0,35 0,37 0,33

ioconsd B.2 4 11 0,18 0,24 0,29 0,31 0,32 0,32 0,34 0,35 0,35 0,36 0,36 0,37 0,36 0,36 0,36 0,38 0,40 0,43 0,28 0,35 0,38 0,34

iointg B.2 4 12 0,18 0,23 0,27 0,29 0,30 0,30 0,32 0,34 0,33 0,35 0,36 0,37 0,38 0,37 0,37 0,37 0,40 0,42 0,26 0,35 0,38 0,33

hhfinsit12 B.2 4 n.a. 0,20 0,25 0,30 0,32 0,33 0,33 0,34 0,35 0,34 0,34 0,34 0,34 0,35 0,35 0,35 0,36 0,38 0,41 0,29 0,34 0,36 0,33

hhecosit12 B.2 4 n.a. 0,20 0,25 0,30 0,32 0,33 0,33 0,34 0,35 0,34 0,34 0,34 0,34 0,35 0,35 0,35 0,36 0,38 0,41 0,29 0,34 0,36 0,33

majpur12 B.2 4 11 0,21 0,27 0,33 0,35 0,37 0,37 0,38 0,39 0,38 0,38 0,39 0,41 0,42 0,42 0,44 0,45 0,46 0,47 0,32 0,39 0,44 0,38

pritre12 B.2 6 0 0,20 0,24 0,27 0,28 0,29 0,28 0,30 0,31 0,30 0,29 0,29 0,29 0,30 0,30 0,31 0,31 0,33 0,34 0,26 0,30 0,31 0,29sav12 B.2 4 0 0,19 0,25 0,30 0,32 0,33 0,33 0,34 0,35 0,34 0,33 0,34 0,34 0,34 0,35 0,35 0,36 0,38 0,40 0,28 0,34 0,36 0,33

uetot_lm B.4 6 n.a. 0,17 0,22 0,27 0,30 0,31 0,31 0,33 0,35 0,36 0,36 0,38 0,39 0,39 0,39 0,39 0,40 0,43 0,46 0,26 0,36 0,41 0,35

uer_lm B.4 6 n.a. 0,17 0,22 0,27 0,30 0,31 0,31 0,33 0,35 0,36 0,36 0,38 0,39 0,39 0,39 0,39 0,40 0,43 0,46 0,26 0,36 0,41 0,35

Aggregation

Agg-AR(1) 0,29 0,43 0,53 0,57 0,54 0,47 0,53 0,61 0,63 0,61 0,52 0,39 0,37 0,36 0,36 0,37 0,40 0,43 0,47 0,55 0,38 0,47

Agg-ARMA(1,1) 0,29 0,44 0,54 0,56 0,54 0,45 0,52 0,61 0,64 0,61 0,53 0,37 0,32 0,31 0,30 0,31 0,33 0,36 0,47 0,55 0,32 0,45

Agg-AR(12) 0,16 0,24 0,30 0,34 0,34 0,34 0,34 0,37 0,37 0,36 0,34 0,35 0,34 0,33 0,32 0,31 0,33 0,36 0,29 0,35 0,33 0,32

Agg-Seas. Dummies 0,20 0,29 0,36 0,36 0,34 0,32 0,36 0,41 0,43 0,42 0,40 0,39 0,39 0,39 0,39 0,39 0,42 0,45 0,31 0,40 0,40 0,37

Agg-ARMA (identical) 0,16 0,23 0,31 0,35 0,37 0,38 0,39 0,44 0,46 0,49 0,52 0,55 0,54 0,53 0,52 0,53 0,58 0,62 0,30 0,48 0,55 0,44

Agg-ARMA (component-specific) 0,15 0,23 0,30 0,33 0,33 0,34 0,35 0,36 0,35 0,35 0,35 0,37 0,35 0,33 0,31 0,31 0,35 0,38 0,28 0,36 0,34 0,33

Agg-oilusd (identical) 0,14 0,18 0,23 0,26 0,26 0,26 0,25 0,28 0,29 0,32 0,33 0,34 0,33 0,31 0,30 0,29 0,31 0,33 0,22 0,30 0,31 0,28

Agg-oilusd (component-specific) 0,13 0,18 0,22 0,25 0,25 0,25 0,24 0,26 0,25 0,26 0,26 0,27 0,26 0,25 0,23 0,20 0,22 0,25 0,21 0,26 0,24 0,24

Agg-multivariate (component-specific) 0,13 0,17 0,21 0,23 0,24 0,24 0,23 0,23 0,22 0,22 0,23 0,23 0,23 0,23 0,22 0,23 0,27 0,31 0,20 0,23 0,25 0,23

Direct forecasts

Indirect forecasts



Tab le.A.8: RMSFE of energy models; c risis and p re-crisis eva luat ion samp le

Horizon: 1 to 6 7 to 12 13 to 18 1 to 18 Horizon: 1 to 6 7 to 12 13 to 18 1 to 18

Benchmarks Benchmarks

AR(1) 4,43 7,74 8,30 6,83 AR(1) 2,91 4,80 5,53 4,41

ARMA(1,1) 4,45 7,71 8,29 6,82 ARMA(1,1) 2,87 4,76 5,51 4,38

AR(12) 4,86 8,99 9,63 7,83 AR(12) 2,93 4,92 5,77 4,54

Seas. Dummies 4,24 7,62 8,27 6,71 Seas. Dummies 2,82 4,72 5,56 4,37

Univariate (AIC) AR MA Univariate (AIC) AR MA

U.1 9 9 4,70 8,46 8,91 7,36 U.1 6 8 3,54 5,53 5,85 4,97

U.2 2 11 5,47 10,59 10,75 8,94 U.2 8 10 3,02 5,32 6,05 4,80

U.3 4 11 5,43 9,37 9,08 7,96 U.3 8 9 3,41 5,21 6,05 4,89

U.4 9 7 4,92 7,96 8,69 7,19 U.4 10 7 2,95 5,51 5,96 4,81

Univariate (SIC) AR MA Univariate (SIC) AR MA

U.1 5 9 4,77 8,04 8,62 7,15 U.1 6 8 3,54 5,53 5,85 4,97

U.2 1 0 4,14 7,59 8,28 6,67 U.2 2 4 2,93 4,85 5,55 4,44

U.3 2 1 4,43 7,88 8,58 6,96 U.3 6 4 3,06 4,94 5,75 4,58

U.4 1 0 4,04 6,96 7,42 6,14 U.4 1 1 2,89 5,04 5,93 4,62

ADL Specification Y-lags X-lags ADL Specification Y-lags X-lags

oileur B.4 2 12 1,95 3,29 3,62 2,96 oileur B.3 0 12 1,57 2,05 2,24 1,95

oilusd B.4 0 12 1,69 2,40 2,66 2,25 oilusd B.3 0 16 1,67 2,43 2,56 2,22

hwwieur B.2 5 12 1,74 2,67 2,94 2,45 hwwieur B.1 5 12 1,49 1,82 1,89 1,73

hwwicoil B.4 2 12 1,96 3,09 3,38 2,81 hwwicoil B.3 0 14 1,65 1,95 1,99 1,86

hwwienrm B.4 3 12 1,83 2,76 3,01 2,53 hwwienrm B.3 0 14 1,63 1,91 1,91 1,82

hwwi B.2 5 12 1 ,79 2,71 3 ,00 2,50 hwwi B.1 5 12 1 ,46 1,78 1 ,89 1,71

eurusd B.4 1 n.a. 4,04 6,96 7,42 6,14 eurusd B.3 1 n.a. 2,83 4,73 5,57 4,38

iptotencon B.4 1 n.a. 4,04 6,96 7,42 6,14 iptotencon B.3 1 n.a. 2,83 4,73 5,57 4,38

iptotcon B.4 1 1 3,91 5,96 5,66 5,18 iptotcon B.3 1 n.a. 2,83 4,73 5,57 4,38

iptoten B.4 1 1 3,91 6,04 5,72 5,22 iptoten B.3 1 n.a. 2,83 4,73 5,57 4,38

ipcapg B.4 1 n.a. 4,04 6,96 7,42 6,14 ipcapg B.3 1 n.a. 2,83 4,73 5,57 4,38

ipconsg B.4 1 n.a. 4,04 6,96 7,42 6,14 ipconsg B.3 1 n.a. 2,83 4,73 5,57 4,38

ipintgds B.4 1 0 4,28 7,41 7,54 6,41 ipintgds B.3 1 n.a. 2,83 4,73 5,57 4,38

ipener B.4 1 1 3 ,94 6,38 6 ,67 5,66 ipener B.4 11 2 2,84 4,31 4,95 4,03

iocapg B.2 1 7 4,10 5,84 5,01 4,99 iocapg B.1 1 7 2,73 4 ,50 5 ,39 4,21

ioconsd B.4 1 0 4,15 7,24 7,69 6,36 ioconsd B.3 1 0 2,81 4,74 5,58 4,38

iointg B.4 1 2 3,29 4,64 5,17 4,37 iointg B.3 2 2 2,67 4,45 5,18 4,10

uetot_lm B.4 1 n.a. 4,04 6,96 7,42 6,14 uetot_lm B.3 1 n.a. 2,83 4,73 5,57 4,38

uer_lm B.4 1 0 3,87 6,37 6,57 5,60 uer_lm B.3 1 n.a. 2,83 4,73 5,57 4,38

Energy

Crisis Pre-crisis

Tab le.A.9: RMSFE of p roc essed food mod els; c risis and pre-crisis eva luat ion sample



AR(1) 0,78 1,88 2,31 1,66 AR(1) 0,52 0,86 0,96 0,78

ARMA(1,1) 0,75 1,83 2,23 1,60 ARMA(1,1) 0,59 1,08 1,39 1,02

AR(12) 0,84 2,24 2,94 2,01 AR(12) 0,53 0,90 1,16 0,86



U.1 11 9 0,82 2,17 2,81 1,93 U.1 10 1 0,54 0,88 1,04 0,82

U.2 9 10 0,82 2,03 2,58 1,81 U.2 5 5 0,54 0,99 1,28 0,94

U.3 5 9 0,84 2,10 2,67 1,87 U.3 10 9 0,55 0,93 1,12 0,87

U.4 10 2 0,78 1,92 2,48 1,73 U.4 11 11 0,61 1,11 1,35 1,02


U.1 4 2 0,74 1,83 2,28 1,62 U.1 3 1 0,59 1,04 1,17 0,93

U.2 1 1 0,75 1,91 2,45 1,70 U.2 5 5 0,54 0,99 1,28 0,94

U.3 5 1 0,83 2,17 2,78 1,93 U.3 4 3 0,56 0,86 1,00 0,81

U.4 1 1 0,75 1,94 2,56 1,75 U.4 1 5 0,60 1,18 1,57 1,11


oileur B.4 10 n.a. 0,78 1,98 2,59 1,78 oileur B.1 9 n.a. 0,54 0,87 0,99 0,80

oilusd B.4 10 n.a. 0,78 1,98 2,59 1,78 oilusd B.1 9 n.a. 0,54 0,87 0,99 0,80

hwwieur B.4 10 n.a. 0,78 1,98 2,59 1,78 hwwieur B.1 9 n.a. 0,54 0,87 0,99 0,80

hwwixeneur B.4 10 0 0,76 1,91 2,53 1,73 hwwixeneur B.1 9 n.a. 0,54 0,87 0,99 0,80

hwwiarm B.4 10 n.a. 0,78 1,98 2,59 1,78 hwwiarm B.1 9 1 0,54 0,90 1,04 0,83

hwwicer B.4 10 0 0,75 1,84 2,41 1,66 hwwicer B.1 9 0 0,54 0,88 1,00 0,81

hwwienrm B.4 10 n.a. 0,78 1,98 2,59 1,78 hwwienrm B.1 9 n.a. 0,54 0,87 0,99 0,80

hwwifood B.4 10 0 0,75 1,87 2,47 1,69 hwwifood B.1 9 0 0,53 0,85 0,97 0,78

hwwiseed B.4 10 0 0,75 1,86 2,45 1,69 hwwiseed B.1 9 2 0,50 0,75 0,86 0,70

hwwi B.4 10 n.a. 0,78 1,98 2,59 1,78 hwwi B.1 9 n.a. 0,54 0,87 0,99 0,80

eurusd B.1 2 1 0,71 1,72 2,15 1,52 eurusd B.3 2 1 0,46 0,73 0,82 0,67

eer21 B.1 10 n.a. 0,78 1,98 2,59 1,78 eer21 B.1 2 1 0,51 0,79 0,86 0,72

reer21 B.1 10 n.a. 0,78 1,98 2,59 1,78 reer21 B.1 2 1 0 ,51 0,78 0 ,84 0,71

iptotencon B.4 10 n.a. 0,78 1,98 2,59 1,78 iptotencon B.1 9 5 0,56 0,88 1,01 0,81

iptotcon B.1 10 0 0,76 1,91 2,50 1,72 iptotcon B.3 9 n.a. 0,50 0,90 1,15 0,85

iptoten B.4 10 0 0,76 1,91 2,50 1,73 iptoten B.1 9 5 0,56 0,89 1,04 0,83

ipcapg B.4 10 n.a. 0,78 1,98 2,59 1,78 ipcapg B.1 9 5 0 ,55 0 ,89 1 ,07 0,84

ipconsg B.1 10 0 0,78 1,96 2,56 1,76 ipconsg B.1 9 5 0,54 0,88 1,03 0,81

ipintgds B.4 10 n.a. 0,78 1,98 2,59 1,78 ipintgds B.1 9 5 0,57 0,89 0,99 0,81

ipener B.2 10 n.a. 0,78 1,98 2,59 1,78 ipener B.4 2 0 0,47 0,74 0,88 0,70

iocapg B.1 9 0 0,75 1 ,94 2,58 1,76 iocapg B.3 9 0 0 ,50 0,90 1 ,16 0,85


iointg B.3 10 0 0,76 1,93 2,54 1,74 iointg B.1 9 0 0,55 0,88 1,00 0,81

uetot_lm B.3 10 0 0,78 1,96 2,44 1,73 uetot_lm B.4 10 1 0,50 0,89 1,07 0,82

uer_lm B.3 10 0 0,77 1,95 2,49 1,74 uer_lm B.2 2 0 0,46 0,76 0,97 0,73

foodunp B.2 9 0 0,79 2,03 2,62 1,81 foodunp B.1 9 0 0,50 0,81 0,92 0,74

Processed food

Crisis Pre-crisis



33

Tab le A.10: RMSFE of unproc essed food mod els; c risis and p re-crisis evaluation

sample



AR(1) 1,21 1,92 1,88 1,67 AR(1) 1,32 1,80 1,63 1,58

ARMA(1,1) 1,20 1,90 1,87 1,66 ARMA(1,1) 1,31 1,77 1,64 1,57

AR(12) 1,07 1,90 2,04 1,67 AR(12) 1,10 1,73 1,78 1,54Seas. Dummies 0,94 1,73 1,86 1,51 Seas. Dummies 0,92 1,51 1,67 1,36


U.1 10 11 1,06 1,83 1,92 1,60 U.1 10 9 1,14 1,76 1,71 1,54

U.2 2 3 0,94 1,73 1,87 1,51 U.2 3 11 1,13 2,07 2,11 1,77

U.3 9 9 1,01 1,82 1,91 1,58 U.3 10 9 1,17 1,78 1,83 1,59

U.4 4 5 0,97 1,72 1,87 1,52 U.4 3 11 1,23 2,27 2,32 1,94


U.1 7 8 1,14 1,83 1,91 1,63 U.1 10 9 1,14 1,76 1,71 1,54

U.2 2 3 0,94 1,73 1,87 1,51 U.2 2 2 0,97 1,56 1,68 1,41

U.3 0 1 1,07 1,95 2,14 1,72 U.3 0 1 1,10 1,81 1,93 1,61

U.4 2 4 0,95 1,75 1,89 1,53 U.4 2 3 0,98 1,52 1,68 1,39


oileur B.3 1 8 1,14 1,98 2,12 1,75 oileur B.3 0 11 0,76 0,98 1,14 0,96

oilusd B.3 1 8 1,23 2,14 2,29 1,88 oilusd B.3 0 8 0,86 1,23 1,35 1,15


hwwixeneur B .2 1 8 0,97 1,69 1,76 1,47 hwwixeneur B.3 1 n.a. 0,94 1,52 1,66 1,37

hwwiarm B.2 1 10 1,09 1,76 1,61 1,49 hwwiarm B.4 0 11 0,89 1,52 1,65 1,36

hwwicer B.1 11 1 1,07 1,67 1,71 1,48 hwwicer B.3 1 n.a. 0,94 1,52 1,66 1,37


hwwifood B.4 1 n.a. 0,93 1,71 1,84 1,49 hwwifood B.3 1 n.a. 0,94 1,52 1,66 1,37

hwwiseed B.4 1 8 0,86 1,54 1,68 1,36 hwwiseed B.4 1 5 1,02 1,81 2,02 1,62

hwwiexen B.4 1 n.a. 0,93 1,71 1,84 1,49 hwwiexen B.3 0 8 0,95 1,61 1,82 1,46

hwwi B.4 0 8 1,28 2,13 2,25 1,89 hwwi B.3 0 11 0 ,74 1 ,01 1 ,18 0,98

eurusd B.4 1 n.a. 0,93 1,71 1,84 1,49 eurusd B.3 1 n.a. 0,94 1,52 1,66 1,37

eer21 B.4 1 n.a. 0,93 1,71 1,84 1,49 eer21 B.3 0 11 0,93 1,48 1,54 1,32

reer21 B.4 1 n.a. 0,93 1,71 1,84 1,49 reer21 B.3 1 n.a. 0,94 1,52 1,66 1,37

iptotencon B.2 5 13 0,72 2,05 2,82 1,87 iptotencon B.1 5 14 0,99 1,49 1,66 1,38

iptotcon B.2 5 14 0,78 2,12 3,47 2,12 iptotcon B.1 5 14 0,95 1,45 1,60 1,33

iptoten B.1 5 14 0,86 1,89 3,62 2,12 iptoten B.3 1 18 1,11 1,55 1,69 1,45

ipcapg B.1 5 13 0,72 1,13 1,82 1,22 ipcapg B.2 5 14 1,11 1,56 1,67 1,45


ipintgds B.3 1 9 1,66 2,71 2,47 2,28 ipintgds B.1 5 14 0,93 1,58 1,81 1,44

ipener B.4 2 1 0 ,93 1,74 1 ,90 1,52 ipener B.2 1 13 1,11 1,82 1,92 1,62

iocapg B.1 5 13 0,72 1,13 1,82 1,22 iocapg B.3 1 1 0 ,92 1 ,46 1 ,62 1,34


iointg B.4 1 20 1,18 1,82 2,76 1,92 iointg B.1 5 14 0,98 1,54 1,75 1,43

uetot_lm B.3 1 4 0,70 1,05 0,96 0,90 uetot_lm B.3 1 n.a. 0,94 1,52 1,66 1,37

uer_lm B.3 1 5 0,65 1,03 1,04 0,91 uer_lm B.3 1 n.a. 0,94 1,52 1,66 1,37

Unprocessed food

Crisis Pre-crisis



34

Tab le A.11: RMSFE of non-ene rgy ind ustria l good s models; c risis and pre-crisis

evaluation sample



AR(1) 1,53 1,62 0,33 1,16 AR(1) 1,22 1,31 0,40 0,98

ARMA(1,1) 1,51 1,60 0,33 1,15 ARMA(1,1) 1,20 1,29 0,38 0,96

AR(12) 0,17 0,28 0,32 0,26 AR(12) 0,18 0,34 0,39 0,30Seas. Dummies 0,64 0,70 0,30 0,54 Seas. Dummies 0,55 0,60 0,34 0,50


U.1 11 11 0,18 0,29 0,30 0,26 U.1 11 8 0,25 0,55 0,60 0,47

U.2 8 5 0,17 0,28 0,30 0,25 U.2 10 11 0,21 0,37 0,38 0,32

U.3 7 10 0,19 0,27 0,30 0,25 U.3 9 11 0,18 0,35 0,41 0,31

U.4 11 7 0,19 0,28 0,30 0,26 U.4 9 10 0,17 0,32 0,36 0,28


U.1 11 5 0,19 0,29 0,30 0,26 U.1 11 8 0,25 0,55 0,60 0,47

U.2 5 5 0,15 0,26 0,29 0,24 U.2 5 5 0,17 0,31 0,35 0,28

U.3 6 0 0,16 0,29 0,33 0,26 U.3 7 7 0,17 0,30 0,34 0,27

U.4 6 0 0,14 0,27 0,32 0,24 U.4 5 7 0,16 0,31 0,36 0,28


oileur B.4 6 0 0,13 0,26 0,31 0,23 oileur B.1 6 5 0,17 0,26 0,27 0,23

oilusd B.4 6 0 0,13 0,26 0,32 0,24 oilusd B.1 6 5 0,16 0,25 0,27 0,23


hwwiarm B.3 11 1 0,16 0,26 0,28 0,23 hwwiarm B.1 11 5 0,19 0,34 0,39 0,30

hwwicoal B.4 6 n.a. 0,14 0,27 0,32 0,24 hwwicoal B.1 6 1 0,16 0,30 0,35 0,27



hwwiind B.3 11 n.a. 0,17 0,27 0,29 0,24 hwwiind B.4 6 n.a. 0,17 0,32 0,37 0,29

hwwiiost B.3 11 n.a. 0,17 0,27 0,29 0,24 hwwiiost B.3 11 4 0,20 0,31 0,31 0,27

hwwinfm B.4 6 n.a. 0,14 0,27 0,32 0,24 hwwinfm B.4 6 n.a. 0,17 0,32 0,37 0,29

hwwitex B.3 11 10 0,18 0,26 0,29 0,25 hwwitex B.1 6 1 0,17 0,31 0,35 0,27

hwwiexen B.3 11 n.a. 0,17 0,27 0,29 0,24 hwwiexen B.4 6 n.a. 0,17 0,32 0,37 0,29

hwwi B.3 11 0 0 ,16 0,25 0 ,28 0,23 hwwi B.1 11 5 0 ,18 0,28 0 ,28 0,25

eurusd B.4 11 16 0,17 0,28 0,32 0,26 eurusd B.3 11 4 0,20 0,36 0,40 0,32

eer21 B.2 11 24 0,18 0,24 0,25 0,22 eer21 B.3 11 4 0 ,19 0,35 0,39 0,31

eer41 B.3 11 5 0,18 0,27 0,29 0,25 eer41 B.3 11 4 0,18 0,33 0,36 0,29

reer21 B.3 11 5 0,18 0,27 0,29 0,24 reer21 B.3 11 4 0,20 0,36 0,40 0,32

reer41 B.4 6 n.a. 0,14 0,27 0,32 0,24 reer41 B.3 11 4 0,19 0,35 0,38 0,31

iptotencon B.4 6 n.a. 0,14 0,27 0,32 0,24 iptotencon B.1 6 4 0,16 0,31 0,36 0,28

iptotcon B.3 11 n.a. 0,17 0,27 0,29 0,24 iptotcon B.1 6 4 0,16 0,30 0,35 0,27

iptoten B.3 11 n.a. 0,17 0,27 0,29 0,24 iptoten B.2 6 4 0,17 0,32 0,39 0,29

ipcapg B.4 6 n.a. 0,14 0,27 0,32 0,24 ipcapg B.4 6 n.a. 0,17 0,32 0,37 0,29

ipconsg B.1 11 9 0,17 0,22 0,21 0,20 ipconsg B.1 6 4 0 ,16 0,31 0,36 0,27

ipintgds B.3 11 n.a. 0,17 0,27 0,29 0,24 ipintgds B.1 6 4 0,17 0,31 0,36 0,28

ipener B.1 11 5 0,17 0,27 0,29 0,24 ipener B.3 7 n.a. 0,16 0,31 0,36 0,28

iocapg B.3 11 n.a. 0,17 0,27 0,29 0,24 iocapg B.1 6 4 0 ,18 0 ,31 0 ,36 0,28

ioconsd B.3 11 n.a. 0,17 0,27 0,29 0,24 ioconsd B.3 6 8 0,22 0,38 0,42 0,34

iointg B.2 6 1 0,16 0,29 0,33 0,26 iointg B.1 6 4 0,17 0,31 0,35 0,27

hhfinsit12 B.3 11 n.a. 0,17 0,27 0,29 0,24 hhfinsit12 B.1 6 0 0,17 0,31 0,36 0,28

majpur12 B.4 6 n.a. 0,14 0,27 0,32 0,24 majpur12 B.3 11 3 0,17 0,30 0,34 0,27

pritre12 B.4 6 0 0,14 0,27 0,32 0,24 pritre12 B.1 6 n.a. 0,17 0,31 0,36 0,28

sav12 B.3 11 n.a. 0,17 0,27 0,29 0,24 sav12 B.3 11 0 0,17 0,31 0,35 0,28

uetot_lm B.4 6 0 0,13 0,24 0,25 0,21 uetot_lm B.3 7 0 0,16 0,29 0,33 0,26

uer_lm B.4 6 0 0,13 0,24 0,24 0,21 uer_lm B.4 6 n.a. 0,17 0,32 0,37 0,29

Non-energy industrial goods

Crisis Pre-crisis



Tab le A.12: RMSFE of services models; crisis and pre-c risis eva lua tion sample



AR(1) 0,50 0,56 0,51 0,52 AR(1) 0,45 0,46 0,28 0,40

ARMA(1,1) 0,44 0,50 0,50 0,48 ARMA(1,1) 0,40 0,43 0,32 0,38

AR(12) 0,23 0,41 0,56 0,40 AR(12) 0,20 0,34 0,40 0,31



U.1 9 11 0,26 0,41 0,52 0,40 U.1 11 7 0,24 0,32 0,33 0,30

U.2 10 6 0,18 0,37 0,51 0,35 U.2 10 8 0,15 0,25 0,31 0,23

U.3 11 11 0,23 0,41 0,54 0,39 U.3 9 9 0,18 0,26 0,31 0,25

U.4 10 9 0,20 0,40 0,53 0,38 U.4 11 5 0,13 0,23 0,30 0,22


U.1 9 11 0,26 0,41 0,52 0,40 U.1 11 7 0,24 0,32 0,33 0,30

U.2 10 6 0,18 0,37 0,51 0,35 U.2 10 6 0,15 0,25 0,30 0,23

U.3 0 4 0,24 0,45 0,64 0,44 U.3 0 4 0,18 0,35 0,47 0,33

U.4 5 6 0,20 0,38 0,52 0,37 U.4 5 5 0,12 0,21 0,28 0,20


oileur B.3 11 0 0,20 0,38 0,51 0,36 oileur B.4 7 0 0,15 0,26 0,30 0,24

oilusd B.3 11 0 0,20 0,39 0,52 0,37 oilusd B.4 7 0 0,15 0,26 0,32 0,24


hwwixeneur B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwixeneur B.3 11 n.a. 0,15 0,27 0,35 0,26

hwwiarm B.3 11 0 0,19 0,36 0,47 0,34 hwwiarm B.3 11 n.a. 0,15 0,27 0,35 0,26



hwwifood B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwifood B.3 11 1 0,15 0,28 0,36 0,26

hwwiind B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwiind B.3 11 n.a. 0,15 0,27 0,35 0,26

hwwinfm B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwinfm B.3 11 n.a. 0,15 0,27 0,35 0,26

hwwiseed B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwiseed B.4 7 1 0,15 0,29 0,35 0,26

hwwitex B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwitex B.3 11 n.a. 0,15 0,27 0,35 0,26

hwwiexen B.3 11 n.a. 0,19 0,36 0,49 0,35 hwwiexen B.3 11 n.a. 0,15 0,27 0,35 0,26

hwwi B.3 11 2 0 ,20 0,38 0 ,51 0,37 hwwi B.4 7 2 0,15 0,28 0,33 0,25

eurusd B.3 11 0 0,18 0,34 0,46 0,33 eurusd B.3 11 n.a. 0,15 0,27 0,35 0,26

eer21 B.3 11 0 0,18 0,34 0,45 0,32 eer21 B.3 11 0 0,14 0,23 0,26 0,21

eer41 B.3 11 0 0,18 0,34 0,46 0,33 eer41 B.3 11 0 0,14 0,24 0,30 0,23

reer21 B.3 11 0 0,18 0,34 0,45 0,32 reer21 B.3 11 0 0,14 0,23 0,26 0,21

reer41 B.3 11 0 0,18 0,34 0,45 0,32 reer41 B.3 11 0 0,14 0,24 0,28 0,22

iptotencon B.2 11 15 0,31 0,52 0,60 0,48 iptotencon B.3 6 5 0,15 0,27 0,33 0,25

iptotcon B.4 5 12 0,27 0,68 0,97 0,64 iptotcon B.1 11 11 0,16 0,25 0,33 0,25

iptoten B.3 11 n.a. 0,19 0,36 0,49 0,35 iptoten B.1 7 15 0,17 0,24 0,34 0,25

ipcapg B.2 9 15 0,30 0,57 0,71 0,53 ipcapg B.1 11 11 0,19 0,26 0,33 0,26


ipintgds B.2 8 15 0,31 0,57 0,64 0,51 ipintgds B.3 7 5 0,15 0,26 0,33 0,25

ipener B.4 7 n.a. 0,18 0,38 0,54 0,37 ipener B.2 11 17 0,15 0,25 0,32 0,24

iocapg B.4 7 0 0,19 0,40 0,57 0,39 iocapg B.4 7 0 0 ,16 0 ,29 0 ,34 0,26


iointg B.2 5 24 0,29 0,45 0,47 0,40 iointg B.3 7 12 0,19 0,31 0,39 0,30

uetot_lm B.4 8 17 0,26 0,53 0,69 0,49 uetot_lm B.3 11 n.a. 0,15 0,27 0,35 0,26

uer_lm B.4 7 10 0,22 0,34 0,41 0,32 uer_lm B.3 11 n.a. 0,15 0,27 0,35 0,26

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